A new coronavirus disease, called COVID-19, appeared in the Chinese region of Wuhan at the end of
last year; since then the virus spread to other countries, including most of Europe. We propose a
differential equation governing the evolution of the COVID-19. This dynamic equation also describes the evolution of the number of infected people for 13 common respiratory viruses (including
the SARS-CoV-2). We validate our theoretical predictions with experimental data for Italy, Belgium
and Luxembourg, and compare them with the predictions of the logistic model.
Temperature and latitude analysis to predict potential spread and seasonalit...CamilaDuitama
Β
This document analyzes the relationship between temperature, latitude, and the spread of COVID-19. It finds that significant community transmission has occurred primarily along the 30-50Β°N latitude corridor where temperatures have been consistently between 5-11Β°C and relative humidity between 47-79%. Using weather modeling, it predicts areas at increased risk for spread over the coming weeks, noting temperatures will rise in the Northern Hemisphere reducing risk. However, it cautions that predictions are speculative given multiple unconsidered factors and calls for further research integrating epidemiological and earth systems modeling.
Ebola hemorrhagic fever is a disease caused by one of five different Ebola viruses. Four of the strains can cause severe illness in humans and animals. Humans can be infected by other humans if they come in contact with body fluids from an infected person or contaminated objects from infected persons. Humans can also be exposed to the virus, for example, by butchering infected animals. Deadly human Ebola outbreaks have been confirmed in the following countries: Democratic Republic of the Congo (DRC), Gabon, South Sudan, Ivory Coast, Uganda, and Republic of the Congo (ROC), Guinea and Liberia. In this sense, it is of vital importance to analysis the history data and predicts its propagation. More specifically, a model based k-means algorithm to determine the optimal locations of virus delivery is constructed and tested Using Mab-lab programming. By experiment, we find that our model can work well and lead to a relatively accurate prediction, which can help the government forecast the epidemic spread more efficiently
Modeling and Forecasting the COVID-19 Temporal Spread in Greece: An Explorato...Konstantinos Demertzis
Β
This document presents a novel method for modeling and forecasting the temporal spread of COVID-19 in Greece based on complex network analysis. The method develops a spline regression model where the knot vector is determined by community detection in the network representing the time series. The model provides a reliable framework for forecasting that can help inform decision making and management of health resources for fighting COVID-19 in Greece. The analysis finds that Greece's infection curve experienced 5 stages of declining dynamics and showed signs of saturation after 33 days, suggesting Greece's response has been effective at keeping cases and deaths relatively low.
Future Prediction Using Supervised Machine Learning for COVID-19IRJET Journal
Β
This document discusses using machine learning methods to predict future cases of COVID-19. It proposes using the long short-term integrated average (LSTIA) method to predict the number of COVID-19 cases in the next 30 days and examine the effects of preventive measures. The LSTIA method and support vector machine (SVM) and least absolute shrinkage and selection operator (LASSO) algorithms are used to analyze COVID-19 case data and make predictions about newly infected cases, deaths, and recoveries. The document concludes the LSTIA method can accurately predict short-term COVID-19 indicators and provide information to help control measures.
Forecasts for the end of the new coronavirus pandemic in brazil and the worldFernando Alcoforado
Β
The document summarizes predictions from universities in Singapore and Minnesota regarding the end of the COVID-19 pandemic in Brazil and worldwide. Researchers in Singapore predict that 97% of the crisis will end by May 30th, 2020 and 100% by December 2nd, 2020. They predict the pandemic will slow in Brazil by June 6th and health will be recovered by September 6th, 2020. Researchers at the University of Minnesota believe the pandemic may involve repetitive waves over 1-2 years or a severe second wave in late 2020, and that 60-70% of the population needs immunity for it to end. Overall predictions vary in optimism, with Singapore's estimates being more optimistic and Minnesota's acknowledging the pandemic may not end soon.
The level of lactate dehydrogenase and ferritin in the blood of Covid-19 pati...SubmissionResearchpa
Β
1. Blood samples from 40 COVID-19 patients and 20 healthy controls were tested to compare levels of lactate dehydrogenase (LDH) and ferritin.
2. LDH and ferritin levels were significantly higher in COVID-19 patients compared to controls, indicating tissue damage and inflammation.
3. Statistical analysis confirmed that higher LDH and ferritin levels in patients were positively associated with COVID-19, while lower levels in controls were negatively associated.
The document discusses COVID-19 and the potential role of environmental factors in its transmission. It provides details about COVID-19, including that it is caused by SARS-CoV-2 and causes respiratory illness. It then discusses how the virus's behavior and susceptibility can vary in different environments. Factors like relative humidity, material of contaminated surfaces, and air temperature may influence how long the virus survives. The spread of the virus through fecal contamination of water is also a possible transmission route. Researchers are working to understand environmental factors that could affect COVID-19 transmission to help control outbreaks.
This document summarizes research on the relationship between air pollution, climate factors like temperature and humidity, and the spread of viruses. It reviews literature showing links between increased air pollutants like PM2.5 and PM10 and higher risk of influenza-like illness. Studies found COVID-19 transmission was highest at certain temperatures and reduced slightly with higher minimum temperatures. Experiments demonstrated influenza virus transmission was enhanced at cold, dry conditions. The document hypothesizes that air pollution levels in highly industrialized areas like Wuhan, China could have implications for new virus emergence and transmission.
Temperature and latitude analysis to predict potential spread and seasonalit...CamilaDuitama
Β
This document analyzes the relationship between temperature, latitude, and the spread of COVID-19. It finds that significant community transmission has occurred primarily along the 30-50Β°N latitude corridor where temperatures have been consistently between 5-11Β°C and relative humidity between 47-79%. Using weather modeling, it predicts areas at increased risk for spread over the coming weeks, noting temperatures will rise in the Northern Hemisphere reducing risk. However, it cautions that predictions are speculative given multiple unconsidered factors and calls for further research integrating epidemiological and earth systems modeling.
Ebola hemorrhagic fever is a disease caused by one of five different Ebola viruses. Four of the strains can cause severe illness in humans and animals. Humans can be infected by other humans if they come in contact with body fluids from an infected person or contaminated objects from infected persons. Humans can also be exposed to the virus, for example, by butchering infected animals. Deadly human Ebola outbreaks have been confirmed in the following countries: Democratic Republic of the Congo (DRC), Gabon, South Sudan, Ivory Coast, Uganda, and Republic of the Congo (ROC), Guinea and Liberia. In this sense, it is of vital importance to analysis the history data and predicts its propagation. More specifically, a model based k-means algorithm to determine the optimal locations of virus delivery is constructed and tested Using Mab-lab programming. By experiment, we find that our model can work well and lead to a relatively accurate prediction, which can help the government forecast the epidemic spread more efficiently
Modeling and Forecasting the COVID-19 Temporal Spread in Greece: An Explorato...Konstantinos Demertzis
Β
This document presents a novel method for modeling and forecasting the temporal spread of COVID-19 in Greece based on complex network analysis. The method develops a spline regression model where the knot vector is determined by community detection in the network representing the time series. The model provides a reliable framework for forecasting that can help inform decision making and management of health resources for fighting COVID-19 in Greece. The analysis finds that Greece's infection curve experienced 5 stages of declining dynamics and showed signs of saturation after 33 days, suggesting Greece's response has been effective at keeping cases and deaths relatively low.
Future Prediction Using Supervised Machine Learning for COVID-19IRJET Journal
Β
This document discusses using machine learning methods to predict future cases of COVID-19. It proposes using the long short-term integrated average (LSTIA) method to predict the number of COVID-19 cases in the next 30 days and examine the effects of preventive measures. The LSTIA method and support vector machine (SVM) and least absolute shrinkage and selection operator (LASSO) algorithms are used to analyze COVID-19 case data and make predictions about newly infected cases, deaths, and recoveries. The document concludes the LSTIA method can accurately predict short-term COVID-19 indicators and provide information to help control measures.
Forecasts for the end of the new coronavirus pandemic in brazil and the worldFernando Alcoforado
Β
The document summarizes predictions from universities in Singapore and Minnesota regarding the end of the COVID-19 pandemic in Brazil and worldwide. Researchers in Singapore predict that 97% of the crisis will end by May 30th, 2020 and 100% by December 2nd, 2020. They predict the pandemic will slow in Brazil by June 6th and health will be recovered by September 6th, 2020. Researchers at the University of Minnesota believe the pandemic may involve repetitive waves over 1-2 years or a severe second wave in late 2020, and that 60-70% of the population needs immunity for it to end. Overall predictions vary in optimism, with Singapore's estimates being more optimistic and Minnesota's acknowledging the pandemic may not end soon.
The level of lactate dehydrogenase and ferritin in the blood of Covid-19 pati...SubmissionResearchpa
Β
1. Blood samples from 40 COVID-19 patients and 20 healthy controls were tested to compare levels of lactate dehydrogenase (LDH) and ferritin.
2. LDH and ferritin levels were significantly higher in COVID-19 patients compared to controls, indicating tissue damage and inflammation.
3. Statistical analysis confirmed that higher LDH and ferritin levels in patients were positively associated with COVID-19, while lower levels in controls were negatively associated.
The document discusses COVID-19 and the potential role of environmental factors in its transmission. It provides details about COVID-19, including that it is caused by SARS-CoV-2 and causes respiratory illness. It then discusses how the virus's behavior and susceptibility can vary in different environments. Factors like relative humidity, material of contaminated surfaces, and air temperature may influence how long the virus survives. The spread of the virus through fecal contamination of water is also a possible transmission route. Researchers are working to understand environmental factors that could affect COVID-19 transmission to help control outbreaks.
This document summarizes research on the relationship between air pollution, climate factors like temperature and humidity, and the spread of viruses. It reviews literature showing links between increased air pollutants like PM2.5 and PM10 and higher risk of influenza-like illness. Studies found COVID-19 transmission was highest at certain temperatures and reduced slightly with higher minimum temperatures. Experiments demonstrated influenza virus transmission was enhanced at cold, dry conditions. The document hypothesizes that air pollution levels in highly industrialized areas like Wuhan, China could have implications for new virus emergence and transmission.
Incorporate the visual brilliance of COVID 19 Template PowerPoint Presentation Slides to deliver a gripping presentation. Using the coronavirus PPT theme, you can display global epicenters of this pandemic on a world map diagram. With the help of this corona PowerPoint slideshow, you can spread awareness by communicating symptoms of the disease. Demonstrate the healthcare system capacity and the number of cases using the line graph given in the COVID 19 PPT template. The concise dashboard diagrams included in this 2019-nCoV disease PowerPoint presentation are appropriate to showcase key statistics of the pandemic. Novel coronavirus pneumonia PPT slideshow helps you to highlight the major pandemics of the modern era like the 1700s smallpox outbreak. Elucidate country-wise stats related to the disease using the dashboard layout in this severe pneumonia with novel pathogens PowerPoint theme. So, download this COVID-19 PPT presentation to outline the affected areas, precautionary measures, and other fundamentals. https://bit.ly/3gGPcTC
The Importance of Asymptomatic Coronavirus Disease-19 Patients: Never Trust a...asclepiuspdfs
Β
The asymptomatic infectious case is a βsilent client,β one of the most complex and damaging types of client: It is someone who does not provide information; of which we have no information. The silent client, as in the asymptomatic infection, can undermine the business by apparently not being able to address the problem. So how do you manage silent clients, asymptomatic cases? Identifying the points where asymptomatic (silent) cases occur and addressing the situation from a comprehensive perspective. This includes: (1) Preventing contagion and interrupting the transmission process immediately after contact with the virus: Test system, trace, and public health measures: Polymerase chain reaction testing on as many people as possible who have been in contact with infected people which allows the isolation of infected and the tracking and quarantine of their contacts; (2) universal public health measures: Wear a mask in public, wash your hands regularly, stay home when sick, keep a physical distance, and avoid meeting people outside of your home; (3) being so strict with negative cases as with positive ones: The consequences of high rates of false negatives are serious because they allow asymptomatic β and symptomatic β people to transmit diseases; follow-up is recommended, from a clinical point of view β epidemiological, as strict to negative cases as to positive ones; (4) trace back the contacts of the positive cases: search the source of a new case, together with the contacts of that person; and (5) massive and opportunistic tests for the detection of general and specific populations: Rapid response tests for coronavirus disease-19 available to everyone, especially those without symptoms, carried out as mass population screening, to certain groups such as health workers and students, as detection opportunistic in the general practitionerβs consultation, and even self-administered by anyone.
1. The SARS-CoV-2 pandemic continues to spread in India, with the curve not yet flattened and cases still rising. The coming month of July is predicted to see worsening of the pandemic in India.
2. As of July 14th, India has seen over 970,000 total cases and 24,929 deaths, surpassing Russia to become the third most affected country. Around 331,505 cases remain active.
3. Various diagnostic tests and their significance, classifications of COVID-19 disease severity, common radiological findings, and epidemiological data are discussed in detail in the document. Increased awareness and improved hospital facilities are needed to better tackle the pandemic in India.
1) An epidemiological model for COVID-19 was developed to simulate its spread through a population of 100 million people. The model considers people as moving between categories of infected, sick, seriously sick, recovered, etc.
2) Preliminary simulations without intervention show rapid exponential growth, peaking after 3 months with over 1.3 million deaths for a doubling time of 4 days. Even faster growth was seen with a doubling time of 2.66 days.
3) "Herd immunity" and "flattening the curve" strategies are found to be inadequate, as infections exceed the threshold for herd immunity and still overwhelm healthcare systems. Maintaining R0 below 1 through sufficient social distancing is required to control
The susceptible-infected-recovered-dead model for long-term identification o...IJECEIAES
Β
The coronavirus (COVID-19) epidemic has spread massively to almost all countries including Indonesia, in just a few months. An important step to overcoming the spread of the COVID-19 is understanding its epidemiology through mathematical modeling intervention. Knowledge of epidemic dynamics patterns is an important part of making timely decisions and preparing hospitals for the outbreak peak. In this study, we developed the susceptible-infected-recovered-dead (SIRD) model, which incorporates the key epidemiological parameters to model and estimate the long-term spread of the COVID-19. The proposed model formulation is data-based analysis using public COVID-19 data from March 2, 2020 to May 15, 2021. Based on numerical analysis, the spread of the pandemic will begin to fade out after November 5, 2021. As a consequence of this virus attack, the cumulative number of infected, recovered, and dead people were estimated at β 3,200,000, β 3,437,000 and β 63,000 people, respectively. Besides, the key epidemiological parameter indicates that the average reproduction number value of COVID-19 in Indonesia is 7.32. The long-term prediction of COVID-19 in Indonesia and its epidemiology can be well described using the SIRD model. The model can be applied in specific regions or cities in understanding the epidemic pattern of COVID-19.
Incorporate the visual brilliance of COVID 19 Template PowerPoint Presentation Slides to deliver a gripping presentation. Using the coronavirus PPT theme, you can display global epicenters of this pandemic on a world map diagram. With the help of this corona PowerPoint slideshow, you can spread awareness by communicating symptoms of the disease. Demonstrate the healthcare system capacity and the number of cases using the line graph given in the COVID 19 PPT template. The concise dashboard diagrams included in this 2019-nCoV disease PowerPoint presentation are appropriate to showcase key statistics of the pandemic. Novel coronavirus pneumonia PPT slideshow helps you to highlight the major pandemics of the modern era like the 1700s smallpox outbreak. Elucidate country-wise stats related to the disease using the dashboard layout in this severe pneumonia with novel pathogens PowerPoint theme. So, download this COVID-19 PPT presentation to outline the affected areas, precautionary measures, and other fundamentals. https://bit.ly/3yA9QwF
Emergency management 11
Emergency Management
Abstract:
In the month of December, 2019 there was outbreak of pneumonia with unknown reason in Wuhan, China. Wuhan is the center of attention because of the respiratory disorder cause by a virus called Corona and also known as Novel COVID β 19. Validate the existence of this virus was also diagnosed in Wuhan. Then it start spreading all over the world due to the social gatherings. It ultimately take thousands of people towards death. Then after its huge destruction a final step of lockdown is taken up by the government of each country. The animal-to-human transmission was presumed as the main mechanism. It was concluded that the virus could also be transmitted from human-to-human, and symptomatic people are the most frequent source of COVID-19 spread. The virus-host interaction and the evolution of the epidemic, with specific reference to the times when the epidemic will reach its peak.
Introduction:
There is scanty knowledge on the actual pandemic potential of this new SARS-like virus. It might be speculated that SARS-CoV-2 epidemic is grossly underdiagnosed and that the infection is silently spreading across the globe. There are no comparable analogies to corona virus. This virus is not like any of the other epidemiological threats that have emerged in recent decades; it is less fatal but much more contagious.
Distribution of cases by the following:
Β· Time: The outbreak of 2019 novel coronavirus disease (COVID-19) was first reported on December 31, 2019.
Β· Place: the epidemiology of 2019 novel coronavirus disease (COVID-19) in a remote region of China, far from Wuhan, we analyzed the epidemiology of COVID-19 in Gansu Province
Explanation of the research topic (corona virus):
As the outbreak of coronavirus disease 2019 (COVID-19) is rapidly expanding in China and beyond, with the potential to become a world-wide pandemic, real-time analyses of epidemiological data are needed to increase situational awareness and inform interventions. The current most likely hypothesis is that an intermediary host animal has played a role in the transmission. Identifying the animal source of the 2019-nCoV would help to ensure that there will be no further future similar outbreaks with the same virus and will also help understanding the initial spread of the disease.
Numerator (cases of corona virus):
Deaths divided the total of deaths plus recoveries. In early days because of the exponential increase new cases significantly outpace recoveries. Youβre dividing by new cases but the numerator hasnβt had a chance to catch up to the death toll yet to be associated with those cases. If you look at COVID 19 on Feb 17, you get the 2% number only if dividing by total cases. If you look vs recovered cases, itβs 13%.
The WHOβs fatality percentage, announced March 17, 2020, is based simply on the number of deaths g.
Estimates of the severity of coronavirus disease 2019 - a model-based analysisGuy Boulianne
Β
This study used individual-level case data and aggregate case/death counts from China, Hong Kong, Macau, and other countries to estimate key severity metrics for COVID-19, accounting for biases. The researchers estimated that the mean duration from symptom onset to death is 17.8 days, and to hospital discharge is 24.7 days. They estimated the case fatality ratio in China to be 1.38% overall but higher in older age groups, and the infection fatality ratio in China to be 0.66% with increasing risk with age. They also estimated the proportion of infections likely to require hospitalization increases with age up to 18.4% for those aged 80+.
Informe de la OMS sobre el contagio del coronavirus20minutos
Β
The document summarizes evidence on the modes of transmission of the COVID-19 virus. It finds that transmission occurs primarily through respiratory droplets and contact routes when people are within 1 meter of each other. Airborne transmission may occur during specific medical procedures that produce aerosols. Current WHO guidance recommends droplet and contact precautions for those caring for COVID patients, and airborne precautions for aerosol-generating procedures. While some studies have found virus in aerosols and air samples, more research is needed to determine the role of airborne transmission and viability of the virus in aerosols.
COVID 19 is a contagious disease caused by a betacoronavirus, which began in Wuhan, China in late 2019. Until now, this new illness has affected more than 6 million people worldwide, and has claimed more than 300 000 human lives. Governments around the globe were faced with the coronavirus pandemic crisis and designed strategies to slow or halt viral transmission. Measures undertaken included enforcing countrywide lockdowns, banning mass gatherings, closing schools and businesses and halting international travel.
- The COVID-19 outbreak in Italy is following an exponential trend, with the number of infected patients doubling every 3-4 days. If this trend continues, there will be over 30,000 infected patients by mid-March, exceeding Italy's intensive care capacity.
- Between 9-11% of infected patients in Italy have required intensive care, and intensive care needs are also following an exponential trend. If not addressed, intensive care needs could reach several thousand beds by mid-April, far more than currently available.
- The analysis can help political leaders allocate sufficient health-care resources like beds, facilities, and personnel to manage the situation in upcoming weeks. Strict social distancing is needed to potentially reduce new cases and
This document discusses the importance of urologists being aware of the clinical presentation of COVID-19. It notes that some early cases of COVID-19 in Italy were initially attributed to urosepsis by internal medicine physicians due to fever in patients with urological devices. However, these cases were later determined to be pneumonia. The document emphasizes that the symptoms of COVID-19 can overlap with urosepsis, so urologists evaluating patients with fever should consider COVID-19 to avoid missed or delayed diagnoses and unnecessary exposure. Laboratory findings like procalcitonin levels can help differentiate between viral COVID-19 infection and bacterial urosepsis.
This document discusses the COVID-19 pandemic, including its causes, symptoms, effects, and potential applications of technology. It describes how the coronavirus was first identified in Wuhan, China in late 2019 and has since spread globally. Key points covered include how the virus spreads and common symptoms like cough and fever. The wide-ranging economic and social impacts of the pandemic are also summarized, as well as some existing and proposed uses of artificial intelligence and ICT technologies to help monitor, predict, and respond to the outbreak.
Name : Renathan Agustianus
NIM : 20190900012
Major : Industrial Engineering
Faculty : Science and Technology
Courses : Bahasa Inggris 2
Lecturer : Harisa Mardiana
FInal Exam
The document discusses COVID-19, describing what it is, how it spreads, and who is most at risk. It then discusses factors in the environment that can affect the transmission of COVID-19, such as relative humidity, air temperature, and fecal contamination of water. Finally, it provides results of studies on how temperature, humidity, and wind speed can influence the spread and viability of the COVID-19 virus.
COVID-19 AND UROLOGY: A Comprehensive Review of the LiteratureValentina Corona
Β
This article reviews the impact of the COVID-19 pandemic on the practice of urology. It discusses how the pandemic has led to the postponement of non-urgent surgeries and changes in residency training. It also examines the potential effects of COVID-19 on the urinary tract, noting that the kidneys and bladder may be at risk of viral invasion due to the presence of ACE2 receptors. The article reviews recommendations regarding kidney transplantation during the pandemic and reports limited cases of COVID-19 infection in renal transplant recipients.
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...navasreni
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic, LUS is being extensively applied to the evaluation and monitoring....
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...clinicsoncology
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...pateldrona
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic, LUS is being extensively applied to the evaluation and monitoring....
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...georgemarini
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic
Managment Of Long Term Care In Era Covid-19komalicarol
Β
COVID-19 gives the chance to address long-term care categories
that are sometimes disregarded and undervalued, such as nursing
and residential homes, as well as homecare. Each method of delivering long-term care must meet the highest possible standards
of ongoing care and quality of life. More study and evaluation are
needed to aid decision-making and policy-making, particularly on
the cost-effectiveness and cost-quality elements for each country,
region, or system.
Renal failure and Quality ofLlife Indicators in Kidney Transplantationkomalicarol
Β
This article discusses quality of life indicators for patients undergoing kidney transplantation. It reviews several tools used to measure quality of life, including the SF-36, EQ-5D, and KDQOL questionnaires. Overall quality of life is generally improved after a successful kidney transplant compared to dialysis. However, factors like side effects of immunosuppressive drugs and the risk of rejection can still impact quality of life. The article concludes that while transplantation is associated with lower mortality and better quality of life than long-term dialysis, certain patient and treatment factors must be considered when evaluating individual quality of life outcomes.
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Similar to Dynamics of the COVID-19 Comparison between the Theoretical Predictions and the Real Data, and Predictions about Returning to Normal Life
Incorporate the visual brilliance of COVID 19 Template PowerPoint Presentation Slides to deliver a gripping presentation. Using the coronavirus PPT theme, you can display global epicenters of this pandemic on a world map diagram. With the help of this corona PowerPoint slideshow, you can spread awareness by communicating symptoms of the disease. Demonstrate the healthcare system capacity and the number of cases using the line graph given in the COVID 19 PPT template. The concise dashboard diagrams included in this 2019-nCoV disease PowerPoint presentation are appropriate to showcase key statistics of the pandemic. Novel coronavirus pneumonia PPT slideshow helps you to highlight the major pandemics of the modern era like the 1700s smallpox outbreak. Elucidate country-wise stats related to the disease using the dashboard layout in this severe pneumonia with novel pathogens PowerPoint theme. So, download this COVID-19 PPT presentation to outline the affected areas, precautionary measures, and other fundamentals. https://bit.ly/3gGPcTC
The Importance of Asymptomatic Coronavirus Disease-19 Patients: Never Trust a...asclepiuspdfs
Β
The asymptomatic infectious case is a βsilent client,β one of the most complex and damaging types of client: It is someone who does not provide information; of which we have no information. The silent client, as in the asymptomatic infection, can undermine the business by apparently not being able to address the problem. So how do you manage silent clients, asymptomatic cases? Identifying the points where asymptomatic (silent) cases occur and addressing the situation from a comprehensive perspective. This includes: (1) Preventing contagion and interrupting the transmission process immediately after contact with the virus: Test system, trace, and public health measures: Polymerase chain reaction testing on as many people as possible who have been in contact with infected people which allows the isolation of infected and the tracking and quarantine of their contacts; (2) universal public health measures: Wear a mask in public, wash your hands regularly, stay home when sick, keep a physical distance, and avoid meeting people outside of your home; (3) being so strict with negative cases as with positive ones: The consequences of high rates of false negatives are serious because they allow asymptomatic β and symptomatic β people to transmit diseases; follow-up is recommended, from a clinical point of view β epidemiological, as strict to negative cases as to positive ones; (4) trace back the contacts of the positive cases: search the source of a new case, together with the contacts of that person; and (5) massive and opportunistic tests for the detection of general and specific populations: Rapid response tests for coronavirus disease-19 available to everyone, especially those without symptoms, carried out as mass population screening, to certain groups such as health workers and students, as detection opportunistic in the general practitionerβs consultation, and even self-administered by anyone.
1. The SARS-CoV-2 pandemic continues to spread in India, with the curve not yet flattened and cases still rising. The coming month of July is predicted to see worsening of the pandemic in India.
2. As of July 14th, India has seen over 970,000 total cases and 24,929 deaths, surpassing Russia to become the third most affected country. Around 331,505 cases remain active.
3. Various diagnostic tests and their significance, classifications of COVID-19 disease severity, common radiological findings, and epidemiological data are discussed in detail in the document. Increased awareness and improved hospital facilities are needed to better tackle the pandemic in India.
1) An epidemiological model for COVID-19 was developed to simulate its spread through a population of 100 million people. The model considers people as moving between categories of infected, sick, seriously sick, recovered, etc.
2) Preliminary simulations without intervention show rapid exponential growth, peaking after 3 months with over 1.3 million deaths for a doubling time of 4 days. Even faster growth was seen with a doubling time of 2.66 days.
3) "Herd immunity" and "flattening the curve" strategies are found to be inadequate, as infections exceed the threshold for herd immunity and still overwhelm healthcare systems. Maintaining R0 below 1 through sufficient social distancing is required to control
The susceptible-infected-recovered-dead model for long-term identification o...IJECEIAES
Β
The coronavirus (COVID-19) epidemic has spread massively to almost all countries including Indonesia, in just a few months. An important step to overcoming the spread of the COVID-19 is understanding its epidemiology through mathematical modeling intervention. Knowledge of epidemic dynamics patterns is an important part of making timely decisions and preparing hospitals for the outbreak peak. In this study, we developed the susceptible-infected-recovered-dead (SIRD) model, which incorporates the key epidemiological parameters to model and estimate the long-term spread of the COVID-19. The proposed model formulation is data-based analysis using public COVID-19 data from March 2, 2020 to May 15, 2021. Based on numerical analysis, the spread of the pandemic will begin to fade out after November 5, 2021. As a consequence of this virus attack, the cumulative number of infected, recovered, and dead people were estimated at β 3,200,000, β 3,437,000 and β 63,000 people, respectively. Besides, the key epidemiological parameter indicates that the average reproduction number value of COVID-19 in Indonesia is 7.32. The long-term prediction of COVID-19 in Indonesia and its epidemiology can be well described using the SIRD model. The model can be applied in specific regions or cities in understanding the epidemic pattern of COVID-19.
Incorporate the visual brilliance of COVID 19 Template PowerPoint Presentation Slides to deliver a gripping presentation. Using the coronavirus PPT theme, you can display global epicenters of this pandemic on a world map diagram. With the help of this corona PowerPoint slideshow, you can spread awareness by communicating symptoms of the disease. Demonstrate the healthcare system capacity and the number of cases using the line graph given in the COVID 19 PPT template. The concise dashboard diagrams included in this 2019-nCoV disease PowerPoint presentation are appropriate to showcase key statistics of the pandemic. Novel coronavirus pneumonia PPT slideshow helps you to highlight the major pandemics of the modern era like the 1700s smallpox outbreak. Elucidate country-wise stats related to the disease using the dashboard layout in this severe pneumonia with novel pathogens PowerPoint theme. So, download this COVID-19 PPT presentation to outline the affected areas, precautionary measures, and other fundamentals. https://bit.ly/3yA9QwF
Emergency management 11
Emergency Management
Abstract:
In the month of December, 2019 there was outbreak of pneumonia with unknown reason in Wuhan, China. Wuhan is the center of attention because of the respiratory disorder cause by a virus called Corona and also known as Novel COVID β 19. Validate the existence of this virus was also diagnosed in Wuhan. Then it start spreading all over the world due to the social gatherings. It ultimately take thousands of people towards death. Then after its huge destruction a final step of lockdown is taken up by the government of each country. The animal-to-human transmission was presumed as the main mechanism. It was concluded that the virus could also be transmitted from human-to-human, and symptomatic people are the most frequent source of COVID-19 spread. The virus-host interaction and the evolution of the epidemic, with specific reference to the times when the epidemic will reach its peak.
Introduction:
There is scanty knowledge on the actual pandemic potential of this new SARS-like virus. It might be speculated that SARS-CoV-2 epidemic is grossly underdiagnosed and that the infection is silently spreading across the globe. There are no comparable analogies to corona virus. This virus is not like any of the other epidemiological threats that have emerged in recent decades; it is less fatal but much more contagious.
Distribution of cases by the following:
Β· Time: The outbreak of 2019 novel coronavirus disease (COVID-19) was first reported on December 31, 2019.
Β· Place: the epidemiology of 2019 novel coronavirus disease (COVID-19) in a remote region of China, far from Wuhan, we analyzed the epidemiology of COVID-19 in Gansu Province
Explanation of the research topic (corona virus):
As the outbreak of coronavirus disease 2019 (COVID-19) is rapidly expanding in China and beyond, with the potential to become a world-wide pandemic, real-time analyses of epidemiological data are needed to increase situational awareness and inform interventions. The current most likely hypothesis is that an intermediary host animal has played a role in the transmission. Identifying the animal source of the 2019-nCoV would help to ensure that there will be no further future similar outbreaks with the same virus and will also help understanding the initial spread of the disease.
Numerator (cases of corona virus):
Deaths divided the total of deaths plus recoveries. In early days because of the exponential increase new cases significantly outpace recoveries. Youβre dividing by new cases but the numerator hasnβt had a chance to catch up to the death toll yet to be associated with those cases. If you look at COVID 19 on Feb 17, you get the 2% number only if dividing by total cases. If you look vs recovered cases, itβs 13%.
The WHOβs fatality percentage, announced March 17, 2020, is based simply on the number of deaths g.
Estimates of the severity of coronavirus disease 2019 - a model-based analysisGuy Boulianne
Β
This study used individual-level case data and aggregate case/death counts from China, Hong Kong, Macau, and other countries to estimate key severity metrics for COVID-19, accounting for biases. The researchers estimated that the mean duration from symptom onset to death is 17.8 days, and to hospital discharge is 24.7 days. They estimated the case fatality ratio in China to be 1.38% overall but higher in older age groups, and the infection fatality ratio in China to be 0.66% with increasing risk with age. They also estimated the proportion of infections likely to require hospitalization increases with age up to 18.4% for those aged 80+.
Informe de la OMS sobre el contagio del coronavirus20minutos
Β
The document summarizes evidence on the modes of transmission of the COVID-19 virus. It finds that transmission occurs primarily through respiratory droplets and contact routes when people are within 1 meter of each other. Airborne transmission may occur during specific medical procedures that produce aerosols. Current WHO guidance recommends droplet and contact precautions for those caring for COVID patients, and airborne precautions for aerosol-generating procedures. While some studies have found virus in aerosols and air samples, more research is needed to determine the role of airborne transmission and viability of the virus in aerosols.
COVID 19 is a contagious disease caused by a betacoronavirus, which began in Wuhan, China in late 2019. Until now, this new illness has affected more than 6 million people worldwide, and has claimed more than 300 000 human lives. Governments around the globe were faced with the coronavirus pandemic crisis and designed strategies to slow or halt viral transmission. Measures undertaken included enforcing countrywide lockdowns, banning mass gatherings, closing schools and businesses and halting international travel.
- The COVID-19 outbreak in Italy is following an exponential trend, with the number of infected patients doubling every 3-4 days. If this trend continues, there will be over 30,000 infected patients by mid-March, exceeding Italy's intensive care capacity.
- Between 9-11% of infected patients in Italy have required intensive care, and intensive care needs are also following an exponential trend. If not addressed, intensive care needs could reach several thousand beds by mid-April, far more than currently available.
- The analysis can help political leaders allocate sufficient health-care resources like beds, facilities, and personnel to manage the situation in upcoming weeks. Strict social distancing is needed to potentially reduce new cases and
This document discusses the importance of urologists being aware of the clinical presentation of COVID-19. It notes that some early cases of COVID-19 in Italy were initially attributed to urosepsis by internal medicine physicians due to fever in patients with urological devices. However, these cases were later determined to be pneumonia. The document emphasizes that the symptoms of COVID-19 can overlap with urosepsis, so urologists evaluating patients with fever should consider COVID-19 to avoid missed or delayed diagnoses and unnecessary exposure. Laboratory findings like procalcitonin levels can help differentiate between viral COVID-19 infection and bacterial urosepsis.
This document discusses the COVID-19 pandemic, including its causes, symptoms, effects, and potential applications of technology. It describes how the coronavirus was first identified in Wuhan, China in late 2019 and has since spread globally. Key points covered include how the virus spreads and common symptoms like cough and fever. The wide-ranging economic and social impacts of the pandemic are also summarized, as well as some existing and proposed uses of artificial intelligence and ICT technologies to help monitor, predict, and respond to the outbreak.
Name : Renathan Agustianus
NIM : 20190900012
Major : Industrial Engineering
Faculty : Science and Technology
Courses : Bahasa Inggris 2
Lecturer : Harisa Mardiana
FInal Exam
The document discusses COVID-19, describing what it is, how it spreads, and who is most at risk. It then discusses factors in the environment that can affect the transmission of COVID-19, such as relative humidity, air temperature, and fecal contamination of water. Finally, it provides results of studies on how temperature, humidity, and wind speed can influence the spread and viability of the COVID-19 virus.
COVID-19 AND UROLOGY: A Comprehensive Review of the LiteratureValentina Corona
Β
This article reviews the impact of the COVID-19 pandemic on the practice of urology. It discusses how the pandemic has led to the postponement of non-urgent surgeries and changes in residency training. It also examines the potential effects of COVID-19 on the urinary tract, noting that the kidneys and bladder may be at risk of viral invasion due to the presence of ACE2 receptors. The article reviews recommendations regarding kidney transplantation during the pandemic and reports limited cases of COVID-19 infection in renal transplant recipients.
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...navasreni
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The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic, LUS is being extensively applied to the evaluation and monitoring....
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...clinicsoncology
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...pateldrona
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic, LUS is being extensively applied to the evaluation and monitoring....
Can Lung Ultrasound in Patients with Fever of Unknown Origin Detect Early Sig...georgemarini
Β
The increasing interest in Lung Ultrasound (LUS) over the last years led to a great diffusion and better experience in using this technique, which became an essential tool for clinicians. During the current Coronavirus Disease 2019 (COVID-19) pandemic
Similar to Dynamics of the COVID-19 Comparison between the Theoretical Predictions and the Real Data, and Predictions about Returning to Normal Life (20)
Managment Of Long Term Care In Era Covid-19komalicarol
Β
COVID-19 gives the chance to address long-term care categories
that are sometimes disregarded and undervalued, such as nursing
and residential homes, as well as homecare. Each method of delivering long-term care must meet the highest possible standards
of ongoing care and quality of life. More study and evaluation are
needed to aid decision-making and policy-making, particularly on
the cost-effectiveness and cost-quality elements for each country,
region, or system.
Renal failure and Quality ofLlife Indicators in Kidney Transplantationkomalicarol
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This article discusses quality of life indicators for patients undergoing kidney transplantation. It reviews several tools used to measure quality of life, including the SF-36, EQ-5D, and KDQOL questionnaires. Overall quality of life is generally improved after a successful kidney transplant compared to dialysis. However, factors like side effects of immunosuppressive drugs and the risk of rejection can still impact quality of life. The article concludes that while transplantation is associated with lower mortality and better quality of life than long-term dialysis, certain patient and treatment factors must be considered when evaluating individual quality of life outcomes.
A case of childhood Burkitt's lymphoma with gingival swelling as the first sy...komalicarol
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This case report describes a 4-year-old child who presented with gingival swelling as the initial symptom of Burkitt's lymphoma. The child was eventually diagnosed with stage IV Burkitt's lymphoma/leukemia based on bone marrow and genetic testing. After initial chemotherapy, the gingival swelling and right cheek swelling recurred, indicating disease recurrence. The child received further chemotherapy but ultimately passed away half a year later. This case highlights that gingival swelling can be an early oral symptom of systemic disease like Burkitt's lymphoma. Dentists and oral physicians play an important role in identifying signs of systemic conditions through oral examinations.
Neuropsychiatric Profiles of Brivaracetam: A Literature Reviewkomalicarol
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Anti-seizure medications (ASMs) can cause cognitive or behavioral adverse drug reactions, which is a significant consideration
when selecting an appropriate ASM. Brivaracetam (BRV) is a
newer synaptic vesicle protein 2A ligand, which is expected to
have less neuropsychiatric adverse effects due to its mechanism of
action. To understand the impact of BRV on cognition and behavior compared with other ASMs, we conducted literatures searching
from PubMed and MEDLINE databases. After the screening process, a total of two animal studies, one randomized controlled trial, one pooled-analysis of clinical trials, one controlled study and
nine observational studies were included. Animal studies showed
that BRV did not worsen cognition or behavior performance in rodents. Human studies showed that BRV had less cognitive adverse
events compared with other second or third generation ASMs. In
addition, currently available evidence suggests that behavioral disturbance is less common with BRV compared with levetiracetam.
This review revealed that BRV has a limited impact on cognition
and behavior. For patients who are intolerant to levetiracetam
and have levetiracetam-related behavioral side effects, switching
to BRV could be beneficial. However, the heterogeneity between
studies makes the quality of the evidence weak and further trials
are needed to confirm the findings.
Clinical and evolutionary features of SARS CoV-2 infection (COVID-19) in chil...komalicarol
Β
Starting with December 2019 the medical world has faced a
new challenge as a consequence of a new type of coronavirus-2019-nCoV, similar to several familiar strains that determine
a comparable symptomatology (SARS- severe acute respiratory syndrome, MERS- Middle East severe acute respiratory syndrome), subsequently named SARS CoV-2, while the disease it
causes- COVID-19. The virus is of animal origin and through an
intermediate host (probably also a mammal) it suffered genetic
changes thus acquiring human cells receptors. In consequence,
SARS CoV-2 virus affects both children and even more frequently where it determines more severe clinical forms of disease. In
children, COVID-19 has various clinical forms, from asymptomatic ones to severe ones, complicated by multisystem inflammatory
syndrome (MIS-C Multisystem Inflammatory Syndrome β Child
or PIMS - TS (Paediatric Multisystem Inflammatory Syndrome
temporally associated with COVID-19) that sometimes can lead
to death
Viral load and antibody responses in an asymptomatic/minimally symptomatic SA...komalicarol
Β
Asymptomatic patients with severe acute respiratory syndrome
coronavirus 2 (SARS-CoV-2), are silent carriers of the disease. We
aimed to characterize their dynamics of disease occurrence, viral
shedding and antibody responses using a cohort of asymptomatic/
minimally symptomatic patients from Sri Lanka during the first
wave of COVID-19.
Vonlay; A paradigm shift in post endodontic restoration: A case report.komalicarol
Β
Porcelain veneers have long been a popular restorative option that
have evolved into a well- accepted treatment that can be fabricated
in various ways. Onlays are another common treatment modality
used in contemporary dentistry to restore large areas of decay and
to replace old restorations. With the availability of newer highstrength materials such as lithium disilicate and processing technologies like CAD/CAM and heat pressing, dental professionals
are now able to produce highly esthetic, high-strength restorations
that blend seamlessly with the natural dentition while also withstanding posterior occlusal forces. A tooth more complex restoration is required after endodontic treatment when compared to normal tooth restoration, because of factors such as extensive caries,
post-treatment root canal dentin and even the economics condition
of the patient.One such design proposed by Dr.Ronald E Goldstein
is βVeenerlayβor βVonlayβ. Vonlay is a blend of an onlay with an
extended buccal veneer surface for use in premolar region, where
there is sufficient enamel present to bond. This restorative option
requires a much less invasive preparation than a full coverage
crown but provides the same structural benefits. Thus, the aim of
this case report is to present a case of Vonlay following endodontic
treatement of lower mandibular premol
A COVID Journey in Diabetes: T1D Diabetes Patient 44 years - Winning in Insul...komalicarol
Β
Complications of Hypoglycaemia, Hypoglycaemia
and Neuroglycopenia are often encountered by patients treated
with insulin. It is feared by patients and families often leading to
emotional and mental scars and can affect lifestyle and confidence.
Hypoglycaemia can occur in premature babies, persons with hypopituitarism and Addisonβs Disease. Low blood glucose can affect
athletes and the elderly leading to falls. Cases are individual and
often difficult for families, clinicians, lawyers and courts to understand.
Loops Around the Heart β A Giant Snakelike Right Coronary Artery Ectasia with...komalicarol
Β
Coronary artery dilatation is an uncommon finding and is incidentally found during diagnostic coronary angiography or at necropsy.
The pathogenesis of dilatation of coronary arteries is still not very
well understood and therapeutic strategies are not clear. It is useful to know the difference between aneurysm and ectasia. In this
report we demonstrate the diagnostic workup of an asymptomatic
patient with a remarkable snakelike dilatation of the right coronary
artery with unique convolute. For the first time we used intracoronary injection and simultaneous echocardiographic visualization
of contrast agent (Sonovue) to proof a fistula to the coronary sinus.
Like our patient, most of the patients are asymptomatic in absence
of coronary artery disease and we decided on a conservative approach because of his very complex anatomy
Skull Metastasis From Papillary Thyroid Carcinoma : Case Report and Literatur...komalicarol
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Although papillary thyroid carcinoma is a relatively common form of malignancy, metastatic spread to the skull
is exceptional. Here, we report a case of papillary thyroid carcinoma revealed by frontal skull metastasis.
Diabetes and Covid-19 Pandemic - A T1 Patient Perspective - Derek C Beattykomalicarol
Β
A patient treated and cared for by NHS Scotland and NHS England
the author has in his 44 years T1D Diabetes journey experienced
surgery provided by the NHS by way of Vitrectomy, Ophthalmic
laser and correction, and Orthopedic knee correction following
a balance issue associated with IV antibiotic treatment for Otitis
Externa and Osteomyelitis associated with long term T1 Diabetes
with neuropathy. Interestingly IV antibiotic treatment led to glycemic issues offering explanation as to why on occasion glycaemia
abnormalities can occur with antibiotic treatment for infection.
Growth Charts-Curves of Children's Height - How to Construct Themkomalicarol
Β
A person born in 1990, for example, grew to one year old on his/
her birth day in 1991 and 17 years old in 2007. No one grows
to their 17 or 20 years old instantaneously. It takes a long-capricious time of mental and physical activities to grow. As regards
childrenβs milk consumption, for example, school lunch programs
were put into in practice on national scale only in the late 1990s.
Those in their late adolescence in 2007 were not the beneficiaries
of free milk, when they were in primary school.
Dermatological health in the COVID-19 erakomalicarol
Β
COVID-19 and its impact on dermatological health was reviewed
from theoretical and statistical frameworks in the present study. A
cross-sectional and retrospective work was documented with a selection of sources indexed to Scopus, considering the period from
2019 to 2022, as well as the search by keywords. Approaches were
discussed in order to outline a comprehensive model that considered the differences between the parties involved, as well as their
relationships in a risk context. The proposal contributes to the state
of the question in terms of the prediction of contingencies derived
from the probability and affectation of dermatological health
The Importance of Framing at the Beginning of an Review Dialoguekomalicarol
Β
Long-term care of patients with chronic conditions in general practice rarely focuses on the treatment process. A specific interaction
tool, the Review Dialogue (RD), has been developed to integrate
patientsβ health-related problems/risks as well as coping strategies
and to agree upon shared treatment objectives assuming that periodical RDs will help to achieve them. Initiated by the GP, the RD
changes the role expectations of the patient and doctor. Therefore,
the framing of the encounters is of particular importance.
Early detection of interstitial lung disease in asymptomatic patients with 2-...komalicarol
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Pulmonary involvement is a common manifestation of Dermatomyositis (DM), the most frequent histologic pattern being Interstitial Lung Disease (ILD) which is a major contributor to
morbidity and mortality in these patients. Therefore, this disease
should be investigated and it is essential to perform pulmonary
function tests (PFTs) and High-Resolution Computed Tomography
(HRCT) early in the course of the disease to make a definitive
diagnosis. Nowadays, 2-deoxy-2-[18F] fluoro-D-glucose positron
emission tomography/computed tomography
Association between Galectin-3 and oxidative stress parameters with coronary ...komalicarol
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Galectin-3 (Gal-3), as a mediator of inflammation and fibrosis, has been reported to be a biomarker of severity in
coronary artery disease (CAD). The study aimed to assess the relationships between coronary artery disease (CAD) and risk factors,
including parameters of oxidative stress in Tunisian patients CAD.
The risks of using 2,4?dinitrophenol (2,4?DNP) as a weight loss agent: a lite...komalicarol
Β
The prevalence of obesity has steadily increased in response to
changes in diet and physical activity patterns over the past 10
years, becoming one of the leading causes of morbidity and mortality worldwide. In addition, the popularity of social networks
has increased social and cultural pressure for the search for the
βperfect bodyβ. These factors result in the search for fast and unconventional methods of weight loss, such as the use of weight
loss accelerating drugs. 2,4-Dinitrophenol (2-4-DNP or DNP) is
an industrial chemical used to lose weight quickly. Due to its great
potential for toxicity, its use has been banned in several countries
since 1938
Height is a measure of consumption that incorporates nutritional needs: When ...komalicarol
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This document summarizes research on trends in height among children in Japan and South Korea from the mid-20th century onward. It finds that as the food supply and consumption of animal proteins increased in both countries following World War II and the Korean War, children grew taller. However, Japanese children stopped growing taller in the late 1980s while South Korean children continued increasing in height until the mid-2000s, eventually surpassing Japanese children. The author questions explanations that focus only on differences in ethnicity or animal protein consumption, noting changes in consumption of other nutrients may also play a role.
Successful management of a broken stylet retained in tracheobronchial tree-a ...komalicarol
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This case report describes the successful removal of a broken piece of stylet from a patient's right main bronchus during intubation for surgery. During intubation using a video laryngoscope and stylet-guided endotracheal tube, the stylet broke off in the bronchus but was not noticed. Later, a nurse observed the stylet was shorter than expected. Bronchoscopy revealed the broken stylet fragment, which was then extracted without issue. The report discusses the importance of carefully checking equipment before and after intubation procedures to prevent such foreign body issues.
Risk Analysis of Secular Trends for a Later Age at MPV of Weight in an Earthq...komalicarol
Β
The Great East Japan Earthquake occurred in 2011, bringing unprecedented damage to the Tohoku region of Japan. Today, after 11
years, the scars from that tremendous damage remain. The health
damage to young school children has been particularly great. One
may imagine a slowing trend in physical growth from the effects
of that disaster, but no clear findings have been reported.
- Video recording of this lecture in English language: https://youtu.be/Pt1nA32sdHQ
- Video recording of this lecture in Arabic language: https://youtu.be/uFdc9F0rlP0
- Link to download the book free: https://nephrotube.blogspot.com/p/nephrotube-nephrology-books.html
- Link to NephroTube website: www.NephroTube.com
- Link to NephroTube social media accounts: https://nephrotube.blogspot.com/p/join-nephrotube-on-social-media.html
Nutritional deficiency Disorder are problems in india.
It is very important to learn about Indian child's nutritional parameters as well the Disease related to alteration in their Nutrition.
Know the difference between Endodontics and Orthodontics.Gokuldas Hospital
Β
Your smile is beautiful.
Letβs be honest. Maintaining that beautiful smile is not an easy task. It is more than brushing and flossing. Sometimes, you might encounter dental issues that need special dental care. These issues can range anywhere from misalignment of the jaw to pain in the root of teeth.
Are you looking for a long-lasting solution to your missing tooth?
Dental implants are the most common type of method for replacing the missing tooth. Unlike dentures or bridges, implants are surgically placed in the jawbone. In laymanβs terms, a dental implant is similar to the natural root of the tooth. It offers a stable foundation for the artificial tooth giving it the look, feel, and function similar to the natural tooth.
How to Control Your Asthma Tips by gokuldas hospital.Gokuldas Hospital
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Respiratory issues like asthma are the most sensitive issue that is affecting millions worldwide. It hampers the daily activities leaving the body tired and breathless.
The key to a good grip on asthma is proper knowledge and management strategies. Understanding the patient-specific symptoms and carving out an effective treatment likewise is the best way to keep asthma under control.
Travel vaccination in Manchester offers comprehensive immunization services for individuals planning international trips. Expert healthcare providers administer vaccines tailored to your destination, ensuring you stay protected against various diseases. Conveniently located clinics and flexible appointment options make it easy to get the necessary shots before your journey. Stay healthy and travel with confidence by getting vaccinated in Manchester. Visit us: www.nxhealthcare.co.uk
Discover the benefits of homeopathic medicine for irregular periods with our guide on 5 common remedies. Learn how these natural treatments can help regulate menstrual cycles and improve overall menstrual health.
Visit Us:Β https://drdeepikashomeopathy.com/service/irregular-periods-treatment/
Summer is a time for fun in the sun, but the heat and humidity can also wreak havoc on your skin. From itchy rashes to unwanted pigmentation, several skin conditions become more prevalent during these warmer months.
Nano-gold for Cancer Therapy chemistry investigatory projectSIVAVINAYAKPK
Β
chemistry investigatory project
The development of nanogold-based cancer therapy could revolutionize oncology by providing a more targeted, less invasive treatment option. This project contributes to the growing body of research aimed at harnessing nanotechnology for medical applications, paving the way for future clinical trials and potential commercial applications.
Cancer remains one of the leading causes of death worldwide, prompting the need for innovative treatment methods. Nanotechnology offers promising new approaches, including the use of gold nanoparticles (nanogold) for targeted cancer therapy. Nanogold particles possess unique physical and chemical properties that make them suitable for drug delivery, imaging, and photothermal therapy.
2. (Table 1 and Table 3) respectively provide the experimental data
for Italy [1] and for Belgium [2, 3]. They show the number of active
people (i.e., people currently infected by SARS-CoV-2), the
recovered people, and deaths for COVID-19.
We start our theoretical analysis by introducing the definition of the
basic re-production number of an infection R0, defined as the
number of infected people derived from a first case in a population
where all the others are susceptible. So, it is not possible to modify
R0, in any case, but it is possible to get a different effective R1
. This
parameter is strictly linked to the replication time of a virus,
indicated with Β΅i, defined as the time interval after which the
number of infected people has increased by R0 times. (Figure 1)
schematically represents the diffusion dynamics of the virus. By
indicating with N the number of infected people, after n steps we
get2
:
π = π 0
π
Figure 1: Schematic dynamics of respiratory virus in the absence of the lockdown
measures in this graphics, for illustrative purpose only, we set R0 = 3. However, for
SARS-CoV-2, the value of R is 2 even at the beginning of the outbreak in China and
Italy. After a period of time ΞΌ1, an infected individual can infect R0 other
individuals. In turn, after a period ΞΌ2, each of these newly infected individuals can
infect other R0 people, and so on. After n steps the elapsed time is π‘ = β ππ
π
π=1
Table 1: Situation in Italy on 15 May 2020. Columns report the number
of active people (currently infected by SARS-CoV-2), the number of
recovered people, and the number of deceased people.
Date Active Recovered
Decease
d
Total
cases
25-Feb 322 1 10 333
26-Feb 400 3 12 415
27-Feb 650 45 18 713
28-Feb 888 46 21 955
29-Feb 1049 50 29 1128
1-Mar 1577 83 34 1694
2-Mar 1835 149 52 2036
3-Mar 2263 160 79 2502
4-Mar 2706 276 107 3089
5-Mar 3296 414 148 3858
6-Mar 3916 523 197 4636
7-Mar 5061 589 233 5883
8-Mar 7375 622 366 8363
9-Mar 9172 724 463 10359
10-Mar 10149 1004 631 11784
11-Mar 10590 1045 827 12462
12-Mar 12839 1258 1016 15113
13-Mar 14955 1439 1266 17660
14-Mar 17750 1966 1441 21157
15-Mar 20603 2335 1809 24747
16-Mar 23073 2749 2158 27980
17-Mar 26062 2941 2503 31506
18-Mar 28710 4025 2978 35713
19-Mar 33190 4440 3405 41035
20-Mar 37860 5129 4032 47021
21-Mar 42681 6072 4825 53578
22-Mar 46638 7024 5475 59137
23-Mar 50418 7432 6077 63927
24-Mar 54030 8326 6820 69176
25-Mar 57511 9362 7503 74376
5. acmcasereport.com
5
Of course, after n steps, the elapsed time is π‘ = β ππ
π
π=1 and,
if there are M outbreaks of infectious viruses, Eq. (1) can be
cast into the form3
π = ππ 0
π‘
π
β
(2)
with π‘ = 1/π β ππ
π
π=1 Note that the two parameters R0 and Β΅ are
not independent (see, for example, [7-9])4
. It is more convenient
to work in the Euler base e rather than in base R0; in the Euler
base Eq. (2) provides the law of growth of a Malthusian
population [5].
π = π exp(π‘/π) where π =
π
log(π 0)
(3)
In literature, Ο is referred to as the characteristic time of the
exponential trend. So, in the absence of containment measures
the number of infected people follows the exponential law (3).
Let us now analyse Eq. (3) in more dept. We have three possible
scenarios:
1. R0 > 1 (as is the current worldβs situation). For Italy, for
example, before the adoption of (severe) containment measures,
the value of Ο was about π~3.8 days (and Β΅ ~ 2.6 days). In this
case the number of the infected people increases exponentially.
2. R0 = 1 If the infection-capacity of the virus is of the type one-
to-one (i.e., a person infected by SARS-CoV-2 can in turn
infects only another person), we get the stationary situation
corresponding to N = 1. This situation is referred to as the latent
situation i.e., the virus is still present but does not spread. In this
limit case, the SARS-CoV-2 is substantially ineffective.
Scenarios (1) and (2) are illustrated in (Figure 2).
Figure 2: Situation before the lockdown measures. Number of infected people
corresponding to the exponential law. The red line represents the case R0 > 1,
such as the situation before the adoption of lockdown measures. The black line
corresponds to the case R0 = 1, the latent situation in which the virus is
substantially ineffective.
3. 0 < R0 < 1. We may also imagine that the capacity of
infection of SARS-CoV-2 is less than 1. This means that the
virus is no longer able to be spread (e.g., thanks to protective
measures, or to the production of vaccines and anti-virals, or
because people who overcame the disease became immune. In
this case, the value of Ο is negative and the number of infected
people decreases ever time. That is, the infection eventually
disappears. The rate of decrease of the number of infected
people depends on the value of Ο. This scenario is depicted in
(Figure 3).
Figure 3: Number of infected people corresponding to the exponential law.
The red line represents the case R0 < 1. In this situation the number of
infected people decreases exponentially and the virus disappears after a
few weeks.
4. Comparison with the Real Data for COVID-19 before
the Lockdown Measures
From a mathematical point of view, we would like to have
R0 = 1 (or, better, R0 < 1), in Eq. (3) instead of R0 > 1. In
practical terms, this means reducing the frequency of all
involuntary It is understood that the main objective of the
lockdown measures established by most European
governments and health organisations is to reduce the ability
of a virus to spread. contacts with a large number of
2
In this Section we shall follow the definitions and the expressions reported in standard books or thesis dissertation such as, for example, [5, 6].
3
Actually, Eq. (2) applies only if the M outbreaks of the virus are exactly at the same conditions. In general, the correct expression reads π = β π 0
π‘ π
Μπ
β
π
π=0
with π
Μπ indicating the replication time of the virus for the i-th outbreak.
4
In ref. [7], the doubling time is used to calculate R0, by means of the equation R0 = 1 + (Ξ³ + Ο) log (2)/Β΅ where Ξ³ is the duration of the incubation period, Ο
is the duration of the symptomatic period, and Β΅ is the doubling time (see [7]). In this respect, we would also like to mention another excellent work recently
produced by G. Steinbrecher [9] (Figure 2 and 3).
6. acmcasereport.com
6
People, reducing unnecessary movements to avoid enc-
ounters, and to prolong the closure of schools. Although these
measures cannot prevent the spread of the infection in the long
term, they can reduce the number of new infections daily. This
has the benefit of leaving room for seriously-ill patients by
avoiding to overload the healthcare system. We can easily
realise what are the consequences if the lockdown measures
are not set up. To make a comparison between the theoretical
predictions and the experimental data in absence of lockdown
measures, we have to consider the correct reference period.
More specifically, we saw that the number of positive cases
grows in the course of time by following the law (3). Hence,
at the reference time t0, the number of people infected by the
virus is
π0 = πexp(π‘0/π) (4)
After a period of time, say t, Eq. (3) reads
π = π exp(π‘/π) (5)
Hence,
π = π0πexp(π‘ β π‘0/π) (6)
Eq. (6) is the equation that we use for comparing the
mathematical predictions with experimental data during the
initial phase where the spread of SARS- CoV-2, causing the
COVID-19, follows the exponential law, and (t-t0) is our
reference period. For the case of COVID-19 we get (see, for
example, [5, 6])
All infectious outbreaks are exactly at the same conditions. So,
Eq. (2) applies;
R0 = 2;
All the Β΅i are equal with each other: Β΅i = const = Β΅ (see also [5,
7]).
In this case, Β΅ is referred to as the doubling time. So, the
doubling time is the amount of time it takes for a given
quantity to double in size or value at a constant growth rate
[8]. If we do not apply the locking measures, the evolution in
the course of time of the number of infected people is best
approximated by an exponential curve with R = 2, even
though we have to stress that R0 is only associated with the
beginning of the epidemic and, with certain approximations,
with the early stages, but not beyond. (Figure 4 and Figure 5)
respectively show the comparison between the theoretical
predictions and the experimental data for Italy and Belgium
before the lockdown measures. We get Ο β 3.8 days and Β΅ β
2.6 days for Italy, and Ο β 5.2 days and Β΅ β 3.7 days for
Belgium. We conclude this Introduction by mentioning that
there are several methods currently proposed in Literature to
derive by mathematical models, the value of R0. For example,
in ref. [9], we have a short numerical code, written in R-
programming language for statistical computing and graphics,
able to compute the estimated R0 values for the following 17
infectious diseases: Chickenpox (varicella) (Transmission:
Aerosol), Common cold (Transmission: Respiratory
Droplets), COVID-19 (Transmission: Respiratory Droplets),
Diphtheria (Transmission: Saliva), Ebola - 2014 Ebola
outbreak (Transmission:: Body fluids, HIV/AIDS
(Transmission: Body fluids), Influenza - 1918 pandemic
strain (Transmission:: Respiratory Droplets), Influenza - 2009
pandemic strain (Transmission: Respiratory Droplets,
Influenza - seasonal strains (Transmission: Respiratory
Droplets), Measles (Transmission: Aerosol), MERS
(Transmission: Respiratory Droplets), Mumps
(Transmission: Respiratory Droplets), Pertussis
(Transmission: Respiratory Droplets), Polio (Transmission:
Fecal oral route), Rubella (Transmission: Respiratory
Droplets), SARS (Transmission: Respiratory Droplets),
Smallpox (Transmission: Respiratory Droplets). However,
this task is particularly problematic if there are intermediate
vectors between hosts, such as malaria.
This manuscript is organised as follows. Section (2)
determines the dynamic differential equation for the COVID-
19; Section (2.3) compares the theoretical predictions and
experimental data for Italy and Belgium. The differential
equations providing the evolution of the decrease of the
number of people tested positive for COVID-19 can be found
in Section (3); Section (4) concludes. The comparison
between the theoretical predictions of our model and
experimental data for Luxembourg, as well as the solution of
the differential equations in the descending phase for
Luxembourg are reported in Appendix. We may object that
we are dealing data from countries which have passed the
peak of infection, such as South Korea, Iceland or Austria etc.
The situation in other Countries, which may have adopted
other political decisions about the application of the lockdown
measures, may be subject of future works. However, we
would like to mention that several authors are currently
applying our model to other Countries. In this regard, we have
received their pre-prints such as the work cited in Ref. [11].
More specifically, we have received a message where our
model has been used, with success, to analyse data from UK,
USA, NY City, Spain, and Mumbai City. We stress the fact
that this manuscript deals with the spread of SARS-CoV-2
until May 16, 2020, as the objective of this work is to study
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the effect of the strict lockdown measures. After May 2020,
these measures have been modified by the various
Governments, which have decided to introduce less heavy and
much less restrictive lockdown measures5
.
Figure 4: Number of infected people in Italy on the 10th of March 2020 (before
the adoption of lockdown measures). The blue line corresponds to the theoretical
predictions and the black dots correspond to experimental data. The values of
the parameters πππand πππ are πππ β 3.8 days and πππ β 2.6 days, respectively.
Figure 5: Exponential phase in Belgium. The lockdown measures have been
adopted on the 16the of March 2020 (however, initially not so strict as in Italy).
The red line corresponds to the theoretical predictions and the black dots
correspond to experimental data. The values of the parameters ππ΅πΈ and ππ΅πΈ are
ππ΅πΈ β 5.3 days and ππ΅πΈ β 3.7 days, respectively.
5. Modelling the COVID-19 - Virusβ growth
The objective of this section is to determine the coefficients of
the evolutionary differential equation for the COVID-19 (see the
forthcoming Eq. (13)). We also determine the generic analytical
expression for the time-dependent number of infected people
through fitting techniques validated by the Ο2
tests. This
expression is proposed after having previously analysed 12
respiratory infectious diseases caused by viruses [10], in
addition of being solution to the Richardβs differential equation.
5.1 General Background
Letting N represent population size and t represent time, the
Logistic model model is formalised by the differential
equation below:
ππ
ππ‘
= πΌπ (1 β
π
πΎ
) (7)
where Ξ± > 0 defines the grow rate and K > 0 is the carrying
capacity. In this equation, the early, unimpeded growth rate is
modelled by the first term +Ξ±N. The value of the rate Ξ±
represents the proportional increase of the population N in one
unit of time. Later, if the system is closed (i.e. the system is
isolated and, hence, not in contact with a reservoir allowing
the system to exchange individuals), as the population grows
the modulus of the second term, Ξ± N2
/K, becomes almost as
large as the first, until to saturating the exponential growth.
This antagonistic effect is called the bottleneck, and is
modelled by the value of the parameter K. The competition
diminishes the combined growth rate, until the value of N
ceases to grow (this is called maturity of the population). The
solution of Eq. (7) is
π(π‘) =
πΎ
1+π΅exp(βπ‘
π
β )
(8)
where B > 0 is a constant related to the value of N (0). It is
more convenient to rewrite Eq. (8) in terms of the initial
Logistic time t0L defined as
π‘0πΏ = πlogπ΅ (9)
So, Eq. (8) may be cast into the form
π(π‘) =
πΎ
1+exp(β
(π‘βπ‘0πΏ
π
β )
(10)
where Ο is linked to the steepness of the curve. Since the
environmental condi- tions influence the carrying capacity, as
a consequence it can be time-varying, with K(t) > 0, leading
to the following mathematical model (see, for example, [12]):
ππ
ππ‘
= πΌπ (1 β
π
πΎ(π‘)
) (11)
occurs. The phenomenological logistic function is used to
model the evolution of the COVID-19 pandemic in different
Countries. The logistic model is mainly used in More
generally, the growth modelling is well described by
5
The study of the dynamics of COVID-19 when the population is subjected to less restrictive measures is beyond the scope of this work and it will be subject
of future studies.
8. acmcasereport.com
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Richardsβ differential equation (RDE) [13]
ππ
ππ‘
= πΌπ (1 β (
π
πΎ(π‘)
)
π£
) (12)
where Ξ½ > 0 affects near which asymptote maximum growth
epidemiology and provides insights into the transmission
dynamics of the virus. We note, however, to evaluate the
dynamics of transmission of SARS-CoV-2, more refined models
are needed, which take into account specific measures adopted in
each Country [14]. So, let us suppose that the Government
decides to adopt the lockdown measures. After the application of
the lockdown measures the equation may be revised to be
ππ
ππ‘
= πΌπ (1 β (
π
πΎ(π‘)
)
π£
) β π(π‘)π (13)
where c(t) takes into account the degree of effectiveness of the
lockdown measures.
5.2. Determination of the Carrying Capacity and the
Lockdown Coefficient for the COVID-19
According to ref. [15]6
Respiratory viruses remain quiet for
months, inactive but viable, within living cells. Then suddenly
they activate and become virulent as they say, the infectious
capacity grows to a maximum, after which it decreases. The time
duration is about of 2 or 3 months. So we can expect that the
epidemic will soon die out in Italy too. So, there is no valid reason
to think that this coronavirus behaves differently from others
[15]. The present work starts from the following hypothesis: the
SARS-CoV-2 behaves like the other viruses that cause
respiratory diseases. As a consequence, for the COVID-19 case,
functions K(t) and c(t) are determined by performing several
fittings on the growth rate-trends of infection capacity of the
viruses that mainly affect the respiratory system. More
specifically, we considered the following 13 different diseases
caused by 12 different viruses: Whooping Cough (Pertussis),
Swine Flu (H1N1), Bird Flu (Avian Flu H5N1), Enterovirus, Flu
in Children, Flu in Adults, Bacterial Pneumonia, Viral
Pneumonia, Bronchitis, Common Cold (Head Cold), Severe
acute respiratory syndrome (SARS), and MERS (Middle East
Respiratory Syndrome). In all the examined cases, we took into
account the fact that the therapy-induced death rate is greater than
the baseline proliferation rate, then there is the eradication of the
disease. In other words, for the above-mentioned cases the
function
c(t) in Eq. (13) represents the therapy-induced death rate [16, 24].
Of course, this is an oversimplified model of both the growth and
the therapy (e.g., it does not take into account the phenomenon of
clonal resistance). We empirically noticed (according to the Ο2
test) that all these viruses have in common the same growth rate-
trend of infected people (of course, each of these behaviors have
their own growth rate parameters). In particular, we get that the
trends of the total number of infected people by respiratory
viruses (indicated with N), subject to the therapy-induced death
rate, versus time satisfy the following
O.D.E. [10]
ππ
ππ‘
Μ
= πΌπ (1 β
π
πΎπ
) β (
πΌπ‘
Μ2
β1
π‘
Μ
) π with π‘Μ > 1 πΌ1 2
β
β (14)
where we have introduced the dimensionless time ^t β‘ t/t0. The
coefficient
π(π‘) β‘ (
πΌπ‘
Μ2β1
π‘
Μ
) with π‘Μ > 1 πΌ1 2
β
β (15)
is referred to as the average therapy-induced death rate. In our
case the term c(t)N in the dynamic equation represents the
lockdown measures. The lockdown is mainly based on the
isolation of the susceptible individuals, eventually with the
removal of infected people by hospitalisation7
. In the idealised
case,
for πΌπ‘Μ2
> 1, c(t) may be modelled as a linear function of π‘Μ, by
getting
π(π‘Μ) = πΌπ‘Μ (16)
As for the epidemiological explanations relating to the various
modelling of c(t) (constant, linear in time etc.), we refer the reader
to the well-known and extensive literature on the subject (see, for
example, Ref [25] or to the references cited in [26]). Here, we
limit ourselves to give a very intuitive explanation on the physical
meaning of this contribution Immediately after the lockdown
measures have been adopted, i.e. during the very first initial
6
Prof. Roberto Ronchetti is currently working at the Pediatric Clinic of La Sapienza of the University of Rome, at the Policlinico Umberto I and at the S.
Andrea 24 March Hospital where he helped to found, dealt with childhood respiratory diseases, and studied bronchiolitis in particular. In these days he has
studied (with his collaborators) the data available on SARS-CoV-2 in China, in South Korea and now in Italy.
7
It is worth mentioning that initially England did not adopt any lockdown measures believing that the British system be a closed system. Basically, it was
believed that the system be governed by a simply logistic equation with a carrying capacity constant or decreasing in time. However, contrary to the
expectations, in England the carrying capacity did not decrease in time. This induced the British government to adopt the lockdown measures.
9. acmcasereport.com
9
phase, we expect that c(π‘Μ,) is practically constant in time, as these
measures have not yet been able to act effectively. However,
after a short period of time, the positive effects of the lockdown
measures become increasingly efficient and it is intuitive to
expect a linear growth of c(π‘Μ) in time. More specifically, we
expect that, after a short transition period the coefficient c(π‘Μ)
starts to grow linearly in time. Successively, at the leading order,
c(π‘Μ,) will be equal in magnitude to the coefficient of the linear
term (in order to balance the growth rate induced by the linear
term). This because the lockdown measures will be able to
satuarte the exponential growth. Briefly, we expect that the
O.D.E. governing the dynamics of the SARS-CoV-2 is of the
form (14) where c(π‘Μ) = Ξ±π‘Μ, for π‘Μ, > 1/πΌ1 2
β
. Indeed, for values of
time π‘
Μ β 1, the lockdown term in Eq. (14) is able to balance the
exponential grow, which is in agreement with our intuitive
expectations.
From Eq. (14) we get that the time derivative of N vanishes for
N = Ns, with Ns satisfying the equation
ππ
πΎπ
=
ππ‘
Μβππ‘
Μ2+1
ππ‘
Μ
> 0 (17)
By taking into account the inequality reported in Eq. (15), we
get that the O.D.E. (14) is valid in the range
1
πΌ1/2 < π‘Μ <
(1+πΌ 4
β )1/2
πΌ1/2 +
1
2
(18)
Parameters KN and Ξ± depend on the virus in question and on the
external conditions (e.g. in our case, the lockdown measures) to
which the population is subject. In Eq. (14), the term -N2
KN is
the term that tends to saturate the exponential growth. KN is
constant (or decreases) in the course of time since the non-linear
contribution becomes more and more important until saturating
the exponential growth. In our model, the carrying capacity is
kept constant. For large values of the carrying capacity, the
solutions of Eq. (14) reach the plateau at the time π‘Μπππ₯ given by
the expression
π‘Μπππ₯ β‘
π‘πππ₯
π‘0
=
1
πΌ1 2
β +
1
2
(19)
Notice that Ξ± is linked to Β΅. Indeed, as shown in Section 1, during
the exponential period the COVID-19 grows according to the
law (see Eq. (6)):
ππ
ππ‘
Μ
β πΜβ1
π where πΜ β‘
π
Μ
π‘0
(20)
Hence, we get
πΌ β
1
π
Μ
=
log(π 0)
2π
Μ
where πΜ β‘
π
π‘0
(21)
We conclude this Section by mentioning that we may easily
check (numerically) that, for systems having a large carrying
capacity, the solution of Eq. (14) is well fitted by the expression
π β π΄π‘exp(β (π‘ β π‘0)2
π
β ) with π = 2π‘0
2
πΌ
β (22)
The values of parameters A, t0 and Ο depend on the virus in
question. It is convenient to re-write Eq. (20) in dimensionless
form
π β π΄
Μπ‘Μ exp(β (π‘Μ β 1)2
π
Μ
β ) where π΄
Μ β‘ π΄π‘0 π
Μ β‘
π
π‘0
2 (23)
To sum up, according to our model for COVID-19, the
ascending behaviour of the total cases (i.e., the number of
positive cases plus the cumulative number of recovered people
plus the cumulative number of deaths) is given by the solution
of Eq. (14) for 1 πΌ1 2
β
β β€ π‘Μ β€ π‘ΜMax.
Notice that the determination of the O.D.E. (14) is of a
fundamental importance if we wish also to describe the
stochastic process (and the associated Fokker- Planck equation)
where a white noise is added to this O.D.E. According to the
literature nomenclature, we refer to the differential equation (14)
as COVID-19 dynamic model8
.
5.3. Comparison between the Theoretical Predictions and
Experimental Data
For Italy and Belgium one observes two distinct phases related
to the dynamics of the COVID-19, which we classify as before
the adoption of the lockdown measures and after some days after
the adoption of the lockdown measures. The question therefore
naturally arises, of whether these two types of regime are
separated by a well-defined transition. We shall see that this is
indeed the case. We may identify three different periods, which
may be classified as follows:
1.
The exponential period. As seen in Section 1, before the
adoption of lockdown measures, the exponential trend is
the intrinsic behaviour of the grow rate of the COVID-19.
8
Viral dynamics is a field of applied mathematics concerned with describing the progression of viral infections within a host organism (see, for example,
[27].)
10. acmcasereport.com
10
In this period the doubling time Β΅ is a constant parameter
versus time.
1. The transient period. The transient period starts after having
applied the severe lockdown measures. In this period, we
observe a sort of oscillations (or fluctuations) of Β΅ versus time.
In this case the time variation of Β΅(t) reflects the behaviour of
the time effective reproduction number, R(t), defined as the
number of cases generated in the current state of a population,
which does not have to be the uninfected state. Fig. 6 and Fig.
7 show the behaviour of the parameter Β΅ versus time for Italy
and Belgium, respectively. The transient period ends when the
last step of the exponential trend fits real data as good as the
linear trend9
.
2. The bell-shaped period (or the post-transient period). In the
bell-shaped period parameter Β΅ is a (typical) function of time
obtained by using Eq. (14). Several theoretical models can be
used to study the post-transient period (e.g., by using
Gompertzβs law [28]). Here, we use two mathematical models:
the solution of the differential equation (14) and the logistic
model (see, for example, Ref. [16]), and we compare these two
theoretical models with real data for Italy and Belgium.
(Figures 8, 9, 16) (see Appendix) compare the predictions of our
model (blue lines) against the logistic model (red lines) for Italy,
Belgium, and Luxembourg, respectively. Notice that the number
of free parameters of these two models are exactly the same,
since Ξ± and Ο cannot be chosen arbitrarily. More specifically,
a) The logistic model possesses two free parameters: K
and t0L. Notice that parameter Ο is not free since it is
linked to the doubling time Β΅;
b) Also our model possesses two free parameters: KN and
t0. Notice that parameter Ξ± is linked to the doubling time
Β΅ (see Eqs (14) and (18)).
(Figure 8, 9) compare the theoretical predictions, with the
experimental data for Italy and Belgium updated to the 15th of
May 2020. The values of the parameters Ο , KN, and t0L for Eq.
(14) and the parameters Ο , t0L and K for the logistic function are
reported in the figure captions. As we can see, for both Countries
Eq. (14) fits well all the real data from the initial days, while the
logistic model applies only to the first data. The curves reach the
plateau at the time tMax given by Eq. (19). By inserting the values
of the parameters, we get
π‘πππ₯πΌπ β 80 days and π‘πππ₯π΅πΈ β 60 days (24)
corresponding to π‘πππ₯πΌπ β 21 April 2020 and π‘πππ₯π΅πΈ β 2 May
2020 for Italy and Belgium, respectively.
Figure 6: Italian transient period (from the 10th of March 2020 to the 24th of
March 2020). During this period, the doubling time Β΅ oscillates over time. Β΅0
indicates the (constant) doubling time during the exponential period (for Italy
π0 β 2.6 days).
Figure 7: Belgian transient period (from the 17th of March 2020 to the 29th of
March 2020). During this period, the doubling time Β΅ oscillates over time. Β΅0
indicates the (constant) doubling time during the exponential period (for
Belgium π0 β 3.7 days).
6. Modelling the COVID-19 - The Descending Phase
Here, for the descending phase is intended the phase where the
number of the positive cases starts to decrease10
. So, our model
cannot be used for describing also the descending phase since
ππ‘ is the number of the total cases and, during the descending
phase, ππ‘ tends to reach the plateau. The objective of this section
is to determine the trend of the curve of positive people during
the descending phase. This task is accomplished by establishing
9
A numerical condition may be established by using the Ο2
test: the fittings of the two trends are considered both good if, for example, for both trends, the Ο2
-
tests get values β₯ 0.9.
10
We define the number of positive people as the number of people tested positive for COVID- 19, hence, by excluding the number of the deceased people
and the number of people who recovered.
11. acmcasereport.com
11
the appropriate equations for the recovered people and the
deceased people for COVID-19. During the descent phase the
number of active people over time must satisfy a conservation
equation. This allows determining the time-evolution for the
positive people. In the sequel, we denote with rt, dt, and nt the
number of people released from the hospital at the time t, the
total deaths, and the number of positive individuals at time t,
respectively
Figure 8: Situation in Italy on 15 May 2020-before, and 65 days after, the
adoption of lockdown measures. The black dots correspond to experimental
data. The red dotted line corresponds to the situation in Italy before the adoption
of the lockdown measures. The blue and the red solid lines correspond to the
theoretical predictions for Italy according to the solution of Eq. (14) and the
logistic model, respectively. Solution of Eq. (14) fits well all the experimental
data from the initial days (i.e., from the 1st of February 2020), while the logistic
model applies only to the first days. The values of the parameters of Eq. (14)
and the logistic function (10) are: πππ β 3.8 days (πππ = 2.6 days),
πΎπ
ππ
β355250, and π‘0πΌπ β72.5 days for Eq. (14), and π0πΌπ β3.8 days (πππ = 2.6
days), πΎππ = 225000, π‘0πΏπΌπ = 53 days for the Logistic function.
Figure 9: Situation in Belgium on 15 May 2020-before, and 60 days after, the
adoption of lockdown measures. The black dots correspond to real data. The
blue dotted line corresponds to the situation in Belgium before the adoption of
the lockdown measures. The blue and the red solid lines correspond to the
theoretical predictions for Belgium according to the solution of Eq. (14) and the
logistic model, respectively. Solution of Eq. (14) fits well all the experimental
data from the initial days (i.e., from the 29th of February 2020), while the
logistic model applies only to the first data. The values of the parameters of Eq.
(14) and the logistic function (10) are: ππ΅πΈ β 5.3 days (ππ΅πΈ = 3.7 days),
πΎπ
π΅πΈ
β42626, and π‘0π΅πΈ β53.4 days for Eq. (14), and ππ΅πΈ β5.3 days (ππ΅πΈ = 3.7
days), πΎπ΅πΈ = 111000, π‘0πΏπ΅πΈ = 39.5 days for the Logistic function, respectively.
The zone I corresponds to the period before the adoption of the lockdown
measures.
Figure 10: Italy situation. Theoretical predictions (blue line) against the
experimental data (black circles) for the recovered people.
Figure 11: Italy situation. Theoretical predictions (blue line) against the
experimental data (black circles) for the deceased people.
6.1 Number of the Recovered People
We start with the recovered people previously hospitalised. Let
us suppose that a hospital has 50 patients in intensive therapy,
corresponding to its maximum availability capacity. If the
hospital is unable to heal any patient, the growth rate of healed
people is necessarily equal to zero. On the other hand, if the
hospital is able to heal a certain number of people, the places
previously occupied by the sick people will free and other
patients affected by COVID-19 will be able to be hospitalized.
In the latter case, the growth rate of the healed people will rise
thanks to the fact that the hospital is able to heal more and more
patients. This initial phase may be modelled by introducing into
the dynamic equation the term +Ξ³rt, with rt indicating the
number of the recovered people at the time t, previously
hospitalized
12. πππ‘
ππ‘
= πππ‘ (25)
However, it is reasonable to suppose that ΞΆ is constant for low
values of r, whereas, when rt takes more and more large values,
ΞΆ is proportional to Ir, with Ir denoting the number of the
infected people entering in the hospital (and not the total
number of the infected people, which is indicated with nt).
Hence,
π = πΌπ β π½ππΌπ > 0 (26)
The sign minus in Eq. (24) is due to the fact that the recovered
people will continue to grow linearly until when it reaches a
maximum limit i.e. until when the hospital is no longer able to
accept other sick people; this causes a reduction of people who
recover. The competition between these two effects diminishes
the combined growth rate. Hence,
πΌπ <
πΌπ
π½π
(27)
where Ξ²r is linked to the hospitalβs capacity to accept sick
people. To sum up,
πππ‘
ππ‘
= πΌππ(π‘) β π½ππΌπ(π‘ β π)π(π‘) where πΌπ(π‘ β π) = π(π‘) +
π·π(π‘ + π1) ) (28)
r(t) is the number of the recovered people, previously
hospitalised, at the time t who have been infected, in average,
at the time π‘ β π and π·π(π‘ + π1) denotes the number of
deceased people at the hospital at the time π‘ + π1 who have
been infected, in average, at the time π‘ β π (in general, π1 β 0.
Clearly, the number of the recovered people, previously
hospitalised, at the step n (i.e. rn), is linked to the total number
of the recovered people previously hospitalised at the step n
(denoted by hn) by the relation
ππ = βπ β βπβ1 or βπ β ππ
π=π‘/βπ‘
π=1 (with βπ‘ β 1 day) (29)
where we have set h0 = 0
6.1.1. Approximated O.D.E. for the Recovered People
Previously Hospitalised
We assume that all the infected people entering in the hospitals
will heal. So
π·π(π‘ + π1) β 0 hence πΌπ(π‘ β π) β π(π‘) (30)
The final O.D.E. for the recovered people reads then
πππ‘
ππ‘
β πΌπ (1 β
1
πΎπ
ππ‘) ππ‘ (31)
where πΎπ is the hospitalβs capacity, which we assume to be a
time-independent parameter. It should be kept in mind that,
under this approximation, the equation for the number of
recovered people is in itself and independent of the equations
for the other variables (i.e. for nt and dt)12
.
6.1.2. O.D.E. for the Total Recovered People
At the first approximation, the O.D.E. for the total recovered
people Rt (i.e. the total individuals having survived the disease)
is trivially obtained by considering that the rate of Rt is
approximatively proportional to the number of the infected
people nt at time t i.e.13
.
ππ π‘
ππ‘
= πππ‘ (32)
However, it is useful to clarify the following. In Eqs (27), ht
stands for the total number of the recovered people previously
hospitalised whereas the variable Rt in Eq. (30) is the total
number of the recovered people (i.e. the number of the
recovered people previously hospitalised, plus the number of
the asymptomatic people, plus the infected people who have
been recovered without being previously hospitalised). The
natural question is: βhow can we count Rt and compare this
variable with the real data ?β. The current statistics, produced
by the Ministries of Health of various Countries, concern the
people released from the hospitals. A part from Luxembourg
(where the entire population has been subject to the COVID-
19-test), no other Countries are in a condition to provide
statistics regarding the total people recovered by COVID-19.
Hence, it is our opinion that the equation for Rt, is not useful
since it is practically impossible to compare Rt with the
experimental data.
6.2. Equation for the Deceased People
The rate of deceased people per unit time is modelled by the
following dimensionless equation
π
ππ‘
Μ
ππ‘ = πΌππ(π‘βπ‘π) β π½ππ(π‘βπ‘π)
2
(33)
The meaning of Eq. (31) is the following. Manifestly, the rate
of deaths is proportional to the number of active people
11
We draw the attention of the reader that in this manuscript Nt (capital letter) represents the number of the total cases at time t, whereas nt (small letter) refers
to the number of the positive individuals at time t.
13. However, individuals infected by SARS-CoV-2 do not die
instantly since the rate of deaths at time t is proportional to the
people who were infected at an earlier time t β td (td > 0) with
td denoting the time-delay. We indicate with Ξ±d the, time-
independent, constant proportional to the increase of the deaths
dt. The second term, βπ½ππ(π‘βπ‘π)
2
, models the presence of the
lockdown measures, having the effect of saturating
the rate of infected people and, consequently, of deaths. Indeed,
in the absence of lockdown measures, we may approximatively
write
π
ππ‘
Μ
ππ‘ = πΌππ(π‘βπ‘π) (34)
with Ξ±r denoting a positive constant. The purpose of the
lockdown measures is to decrease the number of infected
people, and therefore deaths. We may assume that the effect of
the lockdown measures is proportional to π(π‘βπ‘π) such as to
dampen the linear growth of the mortality rate. In other terms,
we get
πΌπ β πΌπ β π½ππ(π‘βπ‘π) (35)
which combined with Eq. (34) gives Eq. (33).
6.3 Equation for the Positive People
Of course, during the descent phase, the number of active
people nt satisfies a simple law of conservation: If we are in the
situation where there are no longer new cases of people tested
positive for COVID-19 and if we assume that the active people
cannot leave their country of origin (or else, if they do, they will
be rejected by the host Country), then the number of infected
people cannot but decrease either because some people are
deceased or because others have been recovered. In
mathematical terms
ππ‘ = π0 β (βπ‘ β β0) β (ππ‘ β π0) = ππππ₯ β βπ‘ β ππ‘ (36)
with h0, d0 and t0 denoting the values of ht, dt and nt evaluated
at the time
t = tMax (see Eq. (19) i.e., the time that maximises the number
of the total cases), respectively. It should be noted that the
conservation law (36) applies only when there are no longer
new cases of people tested positive to COVID- 1914. Here,
by the descending phase we mean the phase where Eq. (36)
applies. To sum up, the equations describing the descending
phase are
π
ππ‘
Μ
ππ‘ = πΌπππ‘ (1 β
ππ‘
πΎπ
) with ππ‘=π‘πππ₯
= π0 (37)
π
ππ‘
Μ
ππ‘ = πΌππ(π‘βπ‘π) β π½ππ(π‘βπ‘π)
2
with ππ‘=π‘πππ₯
= π0
ππ‘ = ππππ₯ β βπ‘ β ππ‘ with πβ = 0
βπ‘ = β ππ
π=π‘/βπ‘
π=1 with βπ‘ β 1 day
with tMax given by Eq. (19). Notice that the first two equations
of system (37) are valid also during the ascending-phase. Of
course,
in this case, the initial conditions are rt=0 = 0, dt=0 = 0 and nt=0.
Hence, during the ascending phase the evolution equations are
π
ππ‘
Μ
ππ‘ = πΌπππ‘ (1 β
ππ‘
πΎπ
) with ππ‘=0 = 0 (38)
π
ππ‘
Μ
ππ‘ = πΌππ(π‘βπ‘π) β π½ππ(π‘βπ‘π)
2
with ππ‘=0 = 0
ππ‘ = ππ‘ β βπ‘ β ππ‘ with ππ‘=0 = 0
π
ππ‘
Μ
ππ‘ = πΌππ‘ (1 β
ππ‘
πΎπ
) β (
πΌπ‘2
Μβ1
π‘
Μ
) ππ‘
βπ‘ = β ππ
π=π‘/βπ‘
π=1 with βπ‘ β 1 day
According to our expectations, by solving numerically
system (38), with good
approximation, we get
ππ‘ β π(π‘βπ‘π) (39)
12
Eq. (31) models a hospitalβs ability to heal people and, by no means, it must be linked to the number of people tested positive for COVID-19 or to the
mortality rate caused by the SARS-CoV-2.
13
Notice that Eq. (32) is the dynamic equation for the total recovered people adopted in the Susceptible-Infectious-Recovered-Deceased-Model (SIRD-model)
[29]. The comparison between our model with the SIRD-model will be found soon in Ref. [30].
14
So, Eq. (36) does not apply necessarily as soon as the number nt (the number of people tested positive for COVID-19) starts to decrease. Indeed, it may
happen that nt decreases because, for example, the number of new cases of people tested positive is less than the number of the people who have recovered in
the meantime. Conservation law (36) applies only from the moment where the number of new cases of people tested positive is strictly equal to zero.
14. Next, we find the numerical solution of systems (37)-(38) for
Italy and Belgium. A similar analysis for Luxembourg is
reported in Appendix.
6.4. Theoretical Predictions for the Descending Phase
In this subsection, we report the numerical solutions of Eqs
(37)-(38) for Italy and Belgium. The solution for Luxembourg
can be found in the Appendix. Fig. (10) and (11) concern the
Italian situation. They show the numerical solution of Eqs (37)-
(38) for the number of recovered people and deaths,
respectively. These theoretical predictions are plotted against
the experimental data reported in the (Table 1). According to
the theoretical predictions, for Italy we get tIT = 12 days. (Figure
12), illustrates the descendant-phase for Italy.
Figure 12: The descending phase for Italy. According to the theoretical
predictions, after two months the lockdown measures may heavily be lightened
and we can return to normal work. The estimated time-delay is π‘ππ = 12 days
see Eq. (37).
(Figure 13, 14) refer to the Belgian situation. The figures
illustrate the numerical solutions of Eqs (37)-(38) for the
number of recovered people and deaths, respectively. The
theoretical predictions are plotted against the experimental data
reported in the (Table 3). According to the theoretical
predictions, for Belgium we get tBEd = 8.8 days. (Figure 15)
shows the descendant-phase for Belgium.
Figure 13: Belgian situation. Theoretical predictions (blue line) against the
experimental data (black circles) for the recovered people.
Figure 14: Belgian situation. Theoretical predictions (blue line) against the
experimental data (black circles) for the deceased people.
Figure 15: The descending phase for Belgium. According to the theoretical
predictions, after one month the lockdown measures may heavily be lightened
and we can return to normal work. The estimated time delay is π‘π΅πΈπ = 8.8
days see Eq. (37).
Table 3: Situation in Belgium on 15 May 2020. Columns report the number of
active people (currently infected by SARS-CoV-2), the number of recovered
people, and the number of deceased people.
Date Active Recovered Deceased Total cases
29-Feb 1 0 0 1
1-Mar 1 0 0 1
2-Mar 6 0 0 6
3-Mar 13 0 0 13
4-Mar 23 0 0 23
5-Mar 50 0 0 50
6-Mar 109 0 0 109
7-Mar 169 0 0 169
8-Mar 200 0 0 200
9-Mar 239 0 0 239
10-Mar 267 0 0 267
11-Mar 311 0 3 314
15. acmcasereport.com
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12-Mar 396 0 3 399
13-Mar 556 0 3 599
14-Mar 686 0 4 689
15-Mar 881 1 4 886
16-Mar 1052 1 5 1058
17-Mar 1218 20 5 1243
18-Mar 1441 31 14 1486
19-Mar 1619 155 21 1795
20-Mar 2016 204 37 2257
21-Mar 2485 263 67 2815
22-Mar 2986 340 75 3401
23-Mar 3305 350 88 3743
24-Mar 3737 410 122 4269
25-Mar 4234 547 178 4937
26-Mar 5340 675 220 6235
27-Mar 6398 858 289 7284
28-Mar 7718 1063 353 9134
29-Mar 9046 1359 431 10836
30-Mar 9859 1527 513 11899
31-Mar 10374 1696 705 12775
1-Apr 11004 2132 828 13964
2-Apr 11842 2495 1011 15348
3-Apr 12755 2872 1143 16770
4-Apr 13901 3247 1283 18431
5-Apr 14493 3751 1447 19691
6-Apr 15196 3986 1632 20814
7-Apr 16002 4157 2035 22194
8-Apr 16482 4681 2240 23403
9-Apr 17296 5164 2523 24983
10-Apr 18080 5568 3019 26667
11-Apr 18686 5986 3346 28018
12-Apr 19584 6463 3600 29647
13-Apr 19979 6707 3903 30589
14-Apr 20094 6868 4157 31119
15-Apr 22025 7107 4440 33573
7. Conclusions
In this work we studied the spread of SARS-CoV-2 until
when the strict measures have been adopted (i.e. until 16th
May 200). The dynamics of COVID-19 when the population
is under less restrictive lockdown measures will be subject
of future studies. Through fitting techniques previously
performed, caused by viruses, including SARS-CoV-2. The
solution of Eq. (14) provides the number of the total case in
time. Successively, we compared the theoretical predictions,
provided by the solution of Eq. (14) and by the logistic model
(see Eq. (7)), with the real data for Italy and Belgium (for
Luxembourg see Appendix). We saw that the solution of Eq.
(14) is in good agreement with the experimental data since
the beginning of the appearance of the COVID-19; this is not
the case for the logistic model which applies only to the few
last days. We found the days where the maximum number
infected people by COVID-19 will be reached in Italy and
Belgium by parametrising the solution of Eq. (41) with
experimental data: we get, tMaxIT 21 April 2020 and tMaxBE 2 May
2020 for Italy and Belgium, respectively.
We also noted, empirically, that the infection process caused by
SARS-CoV-2 may be divided into three qualitatively different
periods; i.e., the exponential period, the transient period and the
bell-shaped period (or the post-transient period). The solution of
Eq. (14) allows defining more precisely these three periods.
Indeed, we may classify the above periods as follows
The exponential period for 0 β€ π‘Μ β€ π‘ΜπΏπ (40)
The transient period for π‘ΜπΏπ < π‘Μ β€ π‘Μππππ₯
The bell-shaped period for π‘Μ > π‘Μππππ₯
With tLM indicating the dimensionless time when the
lockdown measures are applied and tflex the dimensionless
inflection point of the solution of Eq. (14), respectively. It is
easily checked that, for large values of KN, the value of tΛf lex
satisfies, approximatively, the equation
πΌπ‘Μ3
ππππ₯ β 2πΌπ‘Μ2
ππππ₯ + (πΌ β 3)π‘Μππππ₯ + 2 β 0 with π‘Μππππ₯ β‘
π‘ππππ₯
π‘0
(41)
Hence, according to Eq. (41), the transient period ended on 31
March 2020 for Italy and on 7 April 2020 for Belgium,
respectively. The second part of the work is devoted to
modelling the descending phase, i.e. the decrease of the number
of people tested positive for COVID-19. Also in this case, we
proposed a new set of dynamic differential equations that we
solved numerically. The solution of Eqs (37) (and Eq. (38))
provided valuable information such as the duration of the
COVID-19 epidemic in a given Country and therefore when it
will be possible to return to normal life.
8. Acknowledgments
I am very grateful to Alberto Sonnino from Facebook Calibra
and University College London for comments on late
manuscript, and to Ing. Alessandro Leone from the Italian
16. acmcasereport.com
16
Embassy in Belgium for his suggestions and encouragement.
9. Appendix: Comparison between the Theoretical
Predictions of Eq. (14) and Experimental Data for
Luxembourg
We have stressed the main difference between the closed
systems and the open systems. Luxembourg, due to the
particularly severe lockdown measures adopted by the
government, may be considered, with good approximation, as a
closed system (628108 inhabitants, most of them concentrated
in only one town). Indeed, right from the start, the city of
Luxembourg was literally closed and citizens were unable to
enter and leave the city freely (people who had to enter in the
city for working reasons were obliged to undergo each time the
test that, of course, had to result negative).
Italy, on the other hand may be considered, with a god
approximation, as an open system (60317116 inhabitants
dislocated in all the Country). In Italy, especially during the
initial phase, the citizens of northern Italy moved freely to the
south of Italy, by train, by plans or by car. Only in a second time
the Italian government decided to introduce much more
restrictive measures concerning the movement of citizens from
one region to another.
For the reason mentioned above, it is our opinion that it is very
interesting to analyse these two Countries, Luxembourg and
Italy, which are so different with each other. In this Appendix
we report the comparison between the theoretical predictions of
the COVID-19 model (14) and the real data for Luxembourg
update to 15 May 2020 (see (Figure 16)). In the columns of (table
5) we can find the number of active people (currently infected
by SARS-CoV-2), the number of recovered people, and the
number of deceased people, respectively. The experimental data
have been found in the databases [31, 32]. Luxembourg reached
its peak on 12 April 2020.
Table 4: Situation in Belgium on 15 May 2020. Columns report the number of
active people (currently infected by SARS-CoV-2), the number of recovered
people, and the number of deceased people.
Date Active Recovered Deceased Total cases
16-Apr 22390 7562 4857 34809
17-Apr 23014 7961 5163 36138
18-Apr 23346 8384 5453 37183
19-Apr 24056 8757 5683 38496
20-Apr 25260 8895 5828 39983
21-Apr 25296 9002 5998 40956
22-Apr 26194 9433 6262 41889
23-Apr 26507 9800 6490 42797
24-Apr 27492 10122 6679 44293
25-Apr 27991 10417 6917 45325
26-Apr 28255 10785 7094 46134
27-Apr 28602 10878 7207 46687
28-Apr 29060 10943 7331 47334
29-Apr 29075 11283 7501 47859
30-Apr 29349 11576 7594 48519
1-May 29437 11892 7703 49032
2-May 29541 12211 7765 49517
3-May 29753 12309 7844 49906
4-May 29965 12378 7924 50267
5-May 30052 12441 8016 50509
6-May 29711 12731 8339 50781
7-May 30025 12980 8415 51420
8-May 30289 13201 8521 52011
9-May 30604 13411 8581 52596
10-May 30783 13642 8656 53081
11-May 31045 13697 8707 53449
12-May 31286 13732 8761 53779
13-May 31201 13937 8843 53981
14-May 31274 14111 8903 54288
15-May 31384 14301 8959 54644
16-May 31524 14460 9005 54986
17-May 31598 14630 9052 55280
18-May 31822 14657 9080 55559
19-May 31996 14687 9108 55791
20-May 31986 14847 9150 55983
21-May 32061 14988 9186 56235
22-May 32176 15123 9212 56810
23-May 32418 15155 9237 56810
24-May 32540 15272 9280 57092
25-May 32733 15297 9312 57342
26-May 32801 15320 9334 57455
27-May 32763 15465 9364 57592
28-May 32889 15572 9388 57849
17. acmcasereport.com
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Figure 16: Situation in Luxembourg on 15 May 2020. The black dots
correspond to real data. The red dotted line corresponds to the situation in
Luxembourg before the adoption of the lockdown measures. The blue and the
red solid lines correspond to the theoretical predictions for Luxembourg
according to the solution of Eq. (14) and the logistic model, respectively.
Solution of Eq. (14) fits well all the experimental data from the initial days (i.e.,
from the 29th of February 2020), while the logistic model applies only to the
first data. The values of the parameters of Eq. (14) and the logistic function (10)
are: ππΏππ c3.2 days (ππΏππ= 2.2 days), πΎπ
πΏππ
β6880, and π‘0πΏππ β40 days for Eq.
(14), and ππΏππ 3.2 days (ππΏππ = 2.2 days), πΎπΏππ = 3950, π‘0πΏπΏππ = 30 days for
the Logistic function, respectively. The zone I corresponds to the period before
the adoption of the lockdown measures.
Table 5: Situation in Luxembourg on 15 May 2020. Columns provide the
number of active people (currently infected by SARS-CoV-2), the number of
recovered people, and the number of deceased people.
Date Active Recovered Deceased Total cases
29-Feb 1 0 0 1
1-Mar 1 0 0 1
2-Mar 1 0 0 1
3-Mar 1 0 0 1
4-Mar 1 0 0 1
5-Mar 2 0 0 2
6-Mar 3 0 0 4
7-Mar 4 0 0 4
8-Mar 5 0 0 5
9-Mar 5 0 0 5
10-Mar 7 0 0 7
11-Mar 7 0 0 7
12-Mar 26 0 0 26
13-Mar 33 0 1 34
14-Mar 50 0 1 51
15-Mar 76 0 1 77
16-Mar 80 0 1 81
17-Mar 139 0 1 140
18-Mar 201 0 2 203
19-Mar 325 6 4 335
20-Mar 474 6 4 484
21-Mar 656 6 8 670
22-Mar 780 10 8 798
23-Mary 857 10 8 875
24-Mar 1081 10 8 1099
25-Mar 1315 10 8 1333
26-Mar 1434 10 9 1453
27-Maryy 1550 40 15 1605
28-Mar 1773 40 18 1831
29-Mar 1889 40 21 1950
30-Mar 1926 40 22 1988
31-Mar 2115 40 23 2178
01-Apryy 2250 40 29 2319
2-Apr 2417 40 30 2487
3-Apr 2081 500 31 2612
4-Apr 2198 500 31 2729
5-Apr 2268 500 36 2804
6-Apr 2302 500 41 2843
7-Apr 2426 500 44 2970
8-Apr 2488 500 46 3034
9-Apr 2563 500 52 3115
10-Apr 2669 500 54 3223
11-Apr 2708 500 62 3270
12-Apr 2715 500 66 3281
13-Apr 2725 500 67 3292
14-Apr 2740 500 67 3307
15-Apr 2778 520 69 3373
Y Attention on the 23rd the figures instead of being given at 9 am are given at
5 pm.
YY Including 1 evacuated from France.
Table 6: Situation in Luxembourg on 15 May 2020. Columns provide the
number of active people (currently infected by SARS-CoV-2), the number of
recovered people, and the number of deceased people.
Date Active Recovered Deceased Total cases
16-Apr 1008 2368 68 3444
17-Apr 919 2489 72 3480
18-Apr 858 2607 72 3537
19-Apr 799 2678 73 3550
20-Apr 759 2724 75 3558
21-Apr 735 2805 78 3618
22-Apr 689 2885 80 3654
23-Apr 619 2963 83 3665
18. acmcasereport.com
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24-Apr 582 3028 85 3695
25-Apr 539 3087 85 3711
26-Apr 532 3103 88 3723
27-Apr 520 3121 88 3729
28-Apr 531 3121 89 3741
29-Apr 546 3134 89 3769
30-Apr 481 3213 90 3784
1-May 497 3213 92 3802
2-May 402 3318 92 3812
3-May 349 3379 96 3824
4-May 327 3405 96 3828
5-May 332 3412 96 3840
6-May 301 3452 98 3851
7-May 254 3505 100 3859
8-May 245 3526 100 3871
9-May 226 3550 101 3877
10-May 199 3586 101 3886
11-May 185 3602 101 3888
12-May 182 3610 102 3894
13-May 172 3629 103 3904
14-May 147 3665 103 3915
15-May 137 3682 104 3923
16-May 127 3699 104 3930
17-May 136 3702 107 3945
18-May 125 3715 107 3947
19-May 131 3718 109 3958
20-May 134 3728 109 3971
21-May 130 3741 109 3980
22-May 124 3748 109 3981
23-May 123 3758 109 3990
24-May 115 3767 110 3992
25-May 102 3781 110 3993
26-May 102 3783 110 3995
27-May 100 3791 110 4001
28-May 95 3803 110 4008
9.1. The Descending Phase for Luxembourg
(Figures 17, 18) refer to the Luxembourg situation. The
figures illustrate the numerical solutions of Eqs (37) -(38)
for the number of recovered people and deaths,
respectively. The theoretical predictions are plotted
against the experimental data, which can be found in the
(Table 5 Figure 19) shows the descending phase for
Luxembourg.
Figure 17: Luxembourg situation. Theoretical predictions (blue line) against
the experimental data (black circles) for the recovered people.
Figure 18: Luxembourg situation. Theoretical predictions (blue line) against
the experimental data (black circles) for the deceased people.
Figure 19: The descending phase for Luxembourg. According to the theoretical
predictions, after one month the lockdown measures may heavily be lightened and
we can return to normal work. The estimated t imedelay is π‘πΏπππ = 15 days see
Eq. (37).
19. acmcasereport.com
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