Lyapunov Functions and Global Properties of SEIR Epidemic ModelAI Publications
The aim of this paper is to analyze an SEIR epidemic model in which prophylactic for the exposed individuals is included. We are interested in finding the basic reproductive number of the model which determines whether the disease dies out or persist in the population. The global attractivity of the disease-free periodic solution is obtained when the basic reproductive number is less than unity and the disease persist in the population whenever the basic reproductive number is greater than unity, i.e. the epidemic will turn out to endemic. The linear and non–linear Lyapunov function of Goh–Volterra type was used to establish the sufficient condition for the global stability of the model.
COVID-19 (Coronavirus Disease) Outbreak Prediction Using a Susceptible-Exposed-Symptomatic Infected-Recovered-Super Spreaders-Asymptomatic Infected-Deceased-Critical (SEIR-PADC) Dynamic Model
The Susceptible-Infectious Model of Disease Expansion Analyzed Under the Scop...cscpconf
This paper presents a model to approach the dynamics of infectious diseases expansion. Our
model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI)
model of disease expansion based on ordinary differential equations (ODE), and a very simple
approach based on both connectivity between people and elementary binary rules that define
the result of these contacts. The SI deterministic compartmental model has been analysed and
successfully modelled by our method, in the case of 4-connected neighbourhood.
THE SUSCEPTIBLE-INFECTIOUS MODEL OF DISEASE EXPANSION ANALYZED UNDER THE SCOP...csandit
This paper presents a model to approach the dynamics of infectious diseases expansion. Our model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI) model of disease expansion based on ordinary differential equations (ODE), and a very simple approach based on both connectivity between people and elementary binary rules that define the result of these contacts. The SI deterministic compartmental model has been analysed and successfully modelled by our method, in the case of 4-connected neighbourhood.
Lyapunov Functions and Global Properties of SEIR Epidemic ModelAI Publications
The aim of this paper is to analyze an SEIR epidemic model in which prophylactic for the exposed individuals is included. We are interested in finding the basic reproductive number of the model which determines whether the disease dies out or persist in the population. The global attractivity of the disease-free periodic solution is obtained when the basic reproductive number is less than unity and the disease persist in the population whenever the basic reproductive number is greater than unity, i.e. the epidemic will turn out to endemic. The linear and non–linear Lyapunov function of Goh–Volterra type was used to establish the sufficient condition for the global stability of the model.
COVID-19 (Coronavirus Disease) Outbreak Prediction Using a Susceptible-Exposed-Symptomatic Infected-Recovered-Super Spreaders-Asymptomatic Infected-Deceased-Critical (SEIR-PADC) Dynamic Model
The Susceptible-Infectious Model of Disease Expansion Analyzed Under the Scop...cscpconf
This paper presents a model to approach the dynamics of infectious diseases expansion. Our
model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI)
model of disease expansion based on ordinary differential equations (ODE), and a very simple
approach based on both connectivity between people and elementary binary rules that define
the result of these contacts. The SI deterministic compartmental model has been analysed and
successfully modelled by our method, in the case of 4-connected neighbourhood.
THE SUSCEPTIBLE-INFECTIOUS MODEL OF DISEASE EXPANSION ANALYZED UNDER THE SCOP...csandit
This paper presents a model to approach the dynamics of infectious diseases expansion. Our model aims to establish a link between traditional simulation of the Susceptible-Infectious (SI) model of disease expansion based on ordinary differential equations (ODE), and a very simple approach based on both connectivity between people and elementary binary rules that define the result of these contacts. The SI deterministic compartmental model has been analysed and successfully modelled by our method, in the case of 4-connected neighbourhood.
MATHEMATICAL MODELLING OF EPIDEMIOLOGY IN PRESENCE OF VACCINATION AND DELAYcscpconf
The Mathematical modeling of infectious disease is currently a major research topic in the public health domain. In some cases the infected individuals may not be infectious at the time of
infection. To become infectious, the infected individuals take some times which is known as latent period or delay. Here the two SIR models are taken into consideration for present analysis where the newly entered individuals have been vaccinated with a specific rate. The analysis of these models show that if vaccination is administered to the newly entering individuals then the system will be asymptotically stable in both cases i.e. with delay and
without delay
A COMPUTER VIRUS PROPAGATION MODEL USING DELAY DIFFERENTIAL EQUATIONS WITH PR...IJCNCJournal
The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal
diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do not consider the varying probabilities of infection or immunity per node. In this paper, we present the application and the simulation results of the pSEIRS model that takes into account the probabilities, and is thus suitable for more realistic scale free networks. In the pSEIRS model, the death rate and the excess death rate are constant for infective nodes. Latent and immune periods are assumed to be constant and the infection rate is assumed to be proportional to I (t) N(t) , where N (t) is the size of the total population and I(t) is the size of the infected population. A node recovers from an infection
temporarily with a probability p and dies from the infection with probability (1-p).
Mathematics Model Development Deployment of Dengue Fever Diseases by Involve ...Dr. Amarjeet Singh
Dengue virus is one of virus that cause deadly disease
was dengue fever. This virus was transmitted through bite of
Aedes aegypti female mosquitoes that gain virus infected by
taking food from infected human blood, then mosquitoes
transmited pathogen to susceptible humans. Suppressed the
spread and growth of dengue fever was important to avoid
and prevent the increase of dengue virus sufferer and
casualties. This problem can be solved with studied
important factors that affected the spread and equity of
disease by sensitivity index. The purpose of this research
were to modify mathematical model the spread of dengue
fever be SEIRS-ASEI type, to determine of equilibrium
point, to determined of basic reproduction number, stability
analysis of equilibrium point, calculated sensitivity index, to
analyze sensitivity, and to simulate numerical on
modification model. Analysis of model obtained disease free
equilibrium (DFE) point and endemic equilibrium point. The
numerical simulation result had showed that DFE, stable if
the basic reproduction number is less than one and endemic
equilibrium point was stable if the basic reproduction
number is more than one.
Sensitivity Analysis of the Dynamical Spread of Ebola Virus DiseaseAI Publications
The deterministic epidemiological model of (S, E, Iu, Id, R) were studied to gain insight into the dynamical spread of Ebola virus disease. Local and global stability of the model are explored for disease-free and endemic equilibria. Sensitivity analysis is performed on basic reproduction number to check the importance of each parameter on the transmission of Ebola disease. Positivity solution is analyzed for mathematical and epidemiological posedness of the model. Numerical simulation was analyzed by MAPLE 18 software using embedded Runge-Kutta method of order (4) which shows the parameter that has high impact in the spread of the disease spread of Ebola virus disease.
Mathematical Model for Infection and Removalijtsrd
The mathematical model of infectious diseases is a tool that has been used to study the mechanisms by which disease spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. We envisaged a community of n individuals comprising at time t, x, susceptible, y infectious in circulation and z individuals who were isolated, dead, or recovered and immune. We further postulated infection and removal rates ßand , so that there wave ßxydt new infections and ydt removals in time tithe simplest way to do this is to introduce a birth parameter µ, so at to give µdt new susceptible in time dt. If the population is to remain stable the arrival of new susceptible must be balanced by an appropriately defined birth rate. The present paper represents the model in special way, in which the infection occurs in human`s body then the resistance of body gradually decays same as motion decays in damped oscillation. On solving the equation of model, we get solution that gives the idea about the seasonal variation in infection. Shukla Uma Shankar "Mathematical Model for Infection and Removal" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-2 , February 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38523.pdf Paper Url: https://www.ijtsrd.com/mathemetics/other/38523/mathematical-model-for-infection-and-removal/shukla-uma-shankar
Modeling the spread of covid 19 infection using a sir model Manish Singh
The objective of this study was to develop The SIR compartmental mathematical model for prediction of COVID-19 epidemic dynamics considering different intervention scenarios which might give insights on the best interventions to reduce the epidemic risk.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
MATHEMATICAL MODELLING OF EPIDEMIOLOGY IN PRESENCE OF VACCINATION AND DELAYcscpconf
The Mathematical modeling of infectious disease is currently a major research topic in the public health domain. In some cases the infected individuals may not be infectious at the time of
infection. To become infectious, the infected individuals take some times which is known as latent period or delay. Here the two SIR models are taken into consideration for present analysis where the newly entered individuals have been vaccinated with a specific rate. The analysis of these models show that if vaccination is administered to the newly entering individuals then the system will be asymptotically stable in both cases i.e. with delay and
without delay
A COMPUTER VIRUS PROPAGATION MODEL USING DELAY DIFFERENTIAL EQUATIONS WITH PR...IJCNCJournal
The SIR model is used extensively in the field of epidemiology, in particular, for the analysis of communal
diseases. One problem with SIR and other existing models is that they are tailored to random or Erdos type networks since they do not consider the varying probabilities of infection or immunity per node. In this paper, we present the application and the simulation results of the pSEIRS model that takes into account the probabilities, and is thus suitable for more realistic scale free networks. In the pSEIRS model, the death rate and the excess death rate are constant for infective nodes. Latent and immune periods are assumed to be constant and the infection rate is assumed to be proportional to I (t) N(t) , where N (t) is the size of the total population and I(t) is the size of the infected population. A node recovers from an infection
temporarily with a probability p and dies from the infection with probability (1-p).
Mathematics Model Development Deployment of Dengue Fever Diseases by Involve ...Dr. Amarjeet Singh
Dengue virus is one of virus that cause deadly disease
was dengue fever. This virus was transmitted through bite of
Aedes aegypti female mosquitoes that gain virus infected by
taking food from infected human blood, then mosquitoes
transmited pathogen to susceptible humans. Suppressed the
spread and growth of dengue fever was important to avoid
and prevent the increase of dengue virus sufferer and
casualties. This problem can be solved with studied
important factors that affected the spread and equity of
disease by sensitivity index. The purpose of this research
were to modify mathematical model the spread of dengue
fever be SEIRS-ASEI type, to determine of equilibrium
point, to determined of basic reproduction number, stability
analysis of equilibrium point, calculated sensitivity index, to
analyze sensitivity, and to simulate numerical on
modification model. Analysis of model obtained disease free
equilibrium (DFE) point and endemic equilibrium point. The
numerical simulation result had showed that DFE, stable if
the basic reproduction number is less than one and endemic
equilibrium point was stable if the basic reproduction
number is more than one.
Sensitivity Analysis of the Dynamical Spread of Ebola Virus DiseaseAI Publications
The deterministic epidemiological model of (S, E, Iu, Id, R) were studied to gain insight into the dynamical spread of Ebola virus disease. Local and global stability of the model are explored for disease-free and endemic equilibria. Sensitivity analysis is performed on basic reproduction number to check the importance of each parameter on the transmission of Ebola disease. Positivity solution is analyzed for mathematical and epidemiological posedness of the model. Numerical simulation was analyzed by MAPLE 18 software using embedded Runge-Kutta method of order (4) which shows the parameter that has high impact in the spread of the disease spread of Ebola virus disease.
Mathematical Model for Infection and Removalijtsrd
The mathematical model of infectious diseases is a tool that has been used to study the mechanisms by which disease spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. We envisaged a community of n individuals comprising at time t, x, susceptible, y infectious in circulation and z individuals who were isolated, dead, or recovered and immune. We further postulated infection and removal rates ßand , so that there wave ßxydt new infections and ydt removals in time tithe simplest way to do this is to introduce a birth parameter µ, so at to give µdt new susceptible in time dt. If the population is to remain stable the arrival of new susceptible must be balanced by an appropriately defined birth rate. The present paper represents the model in special way, in which the infection occurs in human`s body then the resistance of body gradually decays same as motion decays in damped oscillation. On solving the equation of model, we get solution that gives the idea about the seasonal variation in infection. Shukla Uma Shankar "Mathematical Model for Infection and Removal" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-2 , February 2021, URL: https://www.ijtsrd.com/papers/ijtsrd38523.pdf Paper Url: https://www.ijtsrd.com/mathemetics/other/38523/mathematical-model-for-infection-and-removal/shukla-uma-shankar
Modeling the spread of covid 19 infection using a sir model Manish Singh
The objective of this study was to develop The SIR compartmental mathematical model for prediction of COVID-19 epidemic dynamics considering different intervention scenarios which might give insights on the best interventions to reduce the epidemic risk.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Similar to Predicting COVID-19 (Coronavirus Disease) Outbreak Dynamics Using SIR-based Models: Comparative Analysis of SIRD and Weibull-SIRD (20)
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Multi-source connectivity as the driver of solar wind variability in the heli...Sérgio Sacani
The ambient solar wind that flls the heliosphere originates from multiple
sources in the solar corona and is highly structured. It is often described
as high-speed, relatively homogeneous, plasma streams from coronal
holes and slow-speed, highly variable, streams whose source regions are
under debate. A key goal of ESA/NASA’s Solar Orbiter mission is to identify
solar wind sources and understand what drives the complexity seen in the
heliosphere. By combining magnetic feld modelling and spectroscopic
techniques with high-resolution observations and measurements, we show
that the solar wind variability detected in situ by Solar Orbiter in March
2022 is driven by spatio-temporal changes in the magnetic connectivity to
multiple sources in the solar atmosphere. The magnetic feld footpoints
connected to the spacecraft moved from the boundaries of a coronal hole
to one active region (12961) and then across to another region (12957). This
is refected in the in situ measurements, which show the transition from fast
to highly Alfvénic then to slow solar wind that is disrupted by the arrival of
a coronal mass ejection. Our results describe solar wind variability at 0.5 au
but are applicable to near-Earth observatories.
Predicting COVID-19 (Coronavirus Disease) Outbreak Dynamics Using SIR-based Models: Comparative Analysis of SIRD and Weibull-SIRD
1. Presented by Amir Mosavi
Predicting COVID-19 (Coronavirus Disease)
Outbreak Dynamics Using SIR-based Models:
Comparative Analysis of SIRD and Weibull-SIRD
2. Models
A. SIRD Model
In epidemiological studies, it is assumed that total population size is not changing and remain
constant during epidemy. Human factors such as sex, age, social behaviour, and location are
not considered in SIR model which is not completely correct. In COVID-19 pandemic, it is
observed that transmission rate is strongly dependent on social behaviour and habits of
individuals. The SIRD model consist of 4-set of ordinary differential equations (ODE) for
susceptible population (S), infected cases (I), and recovered cases (R), and deceased cases
(D) as follows [10, 11]:
B. Weibull-SIRD Model
The most commonly used Weibull distribution function of two parameter family (k, c) may
be reformulated for infected population of a pandemic as follows [12]:
3. Optimized Weibull-SIRD parameters for COVID-19 in Kuwait
(18 June 2020).
Total
populatio
n
(N)
shape
facto
r (k)
Scale
facto
r (c)
Growt
h rate
(þ)
Recover
y rate
(yRO)
Death
rate
(yDO)
Removin
g rate (yO)
Reproductio
n number
(RO)
R2(S) R2(I) R2(R) R2(D)
555,509 7.1 98.97 0.0786 0.0686 0.0008 0.02719 1.13 0.985 0.975 0.949 0.719
3 5 5 3
Weibull-SIRD model for fitting 4-set of COVID-19 data simultaneously in Kuwait; Top)
Infected, recovered, and deceased population; Bottom) Susceptible population
4. Predicting COVID-19 (Coronavirus Disease)
Outbreak Dynamics Using SIR-based Models:
Comparative Analysis of SIRD and Weibull-SIRD
Ahmad Sedaghat
School of Engineering,
Australian College of Kuwait,
Safat 13015, Kuwait
a.sedaghat@ack.edu.kw
Shahab Band
National Yunlin University of
Science and Technology
Yunlin 64002, Taiwan
shamshirbands@yuntech.edu.tw
Amir Mosavi
School of Economicsand
Business, Norwegian University
of Life Sciences, Norway
amir.mosavi@kvk.uni-obuda.hu
Laszlo Nadai
Kando Kalman Faculty of
Electrical Engineering
Obuda University,
Budapest, Hungary
Abstract— The SIR type models are built by a set of ordinary
differential equations (ODE), which are strongly initial value
dependant. To fit multiple biological data with SIR type equations
requires fitting coefficients of these equations by an initial guess
and applying optimization methods. These coefficients are also
extremely initial value-dependent. In the vast publication of these
types, we hardly see, among simple to highly complicated SIR type
methods, that these methods presented more than a maximum of
two biological data sets. We propose a novel method that
integrates an analytical solution of the infectious population using
Weibull distribution function into any SIR type models. The
Weibull-SIRD method has easily fitted 4 set of COVID-19
biological data simultaneously. It is demonstrated that the
Weibull-SIRD method predictions for susceptible, infected,
recovered, and deceased populations from COVID-19 in Kuwait
and UAE are superior compared with SIRD original ODE model.
The proposed method here opens doors for new deeper studying
of biological dynamic systems with realistic biological data trends
than providing some complicated, cumbersome mathematical
methods with little insight into biological data's real physics.
Keywords— Coronavirus disease, COVID-19; outbreak; SIR
model; epidemiological model; SIRD model; Weibull
I. INTRODUCTION
Since the outbreak of the novel coronavirus (COVID-19) in
Wuhan, China in December 2019, the world has experienced the
worst pandemic in history; not in terms of fatality but in the way
we have used to live and commute around world. Many
researchers and scientists from different discipline have made
efforts to better understand and manage the COVID-19
pandemic. On 15 June 2020, COVID-19 infectious was reported
8,066,465 cases with 437,295 deaths and 4,174,782 recovered
in 215 countries worldwide [1]. Accurate prediction of COVID-
19 dynamics is highly crucial for the governments and health
organizations to better management of the situation. Exact
solutions of SIR model were reported in a number of
publications; although, these solutions hardly fit with actual data
from a pandemic. Bohner et al. [2] provided a nice article on
Bailey’s [3] SIR model's exact solution. In such methods, the
recovered (R) population is ignored when solving susceptible
(S) and infectious (I) equations; hence, we couldn’t fit the
COVID-data with the explicit formulations provided. Harko et
al. [4] have reported exact solutions to SIR model considering
birth and death rates; yet no actual epidemic data were tested
with these solutions. Shabbir et al. [5] and Maliki [6] have both
reported exact solutions to SIS and SIR original ODE equations
reported by Kermack and McKendrick [7]. These special
models included (S) and (I) equations only.
In this paper, we consider SIRD model, which considers
susceptible (S), infected (I), recovered (R), and deceased (D)
ordinary differential (ODE) equations. Providing a formulation
for infectious population using the Weibull function, we can
easily find all explicit solutions to the rest of the equations
without the need to solve ODE. The present formulation
provides fast and robust solutions to SIRD equations and can be
used to optimize the highest prediction of an
epidemic/pandemic. The goodness of fit to the Weibull-SIRD
model for COVID-19 data in Kuwait and UAE is examined
using the determination coefficient (R2). Results of COVID-19
dynamics are discussed for Kuwait and UAE, and the prediction
capability of the new model is presented, and conclusions are
drawn..
II. MATERIALS ANDMETHDOS
A fast and robust mathematical model solution to any new
pandemic outbreak such as COVID-19 is required to reduce
disastrous consequences and equip with appropriate measures.
COVID-19 indicated the gap on human fragility in tackling
biological crisis. Here, we first provide the formulation of SIRD
model base on susceptible, infected, recovered, and deceased
population [8, 9].
5. A. SIRD Model
In epidemiological studies, it is assumed that total population
size is not changing and remain constant during epidemy.
Human factors such as sex, age, social behaviour, and location
are not considered in SIR model which is not completely
correct. In COVID-19 pandemic, it is observed that
transmission rate is strongly dependent on social behaviour and
habits of individuals. The SIRD model consist of 4-set of
ordinary differential equations (ODE) for susceptible
population (S), infected cases (I), and recovered cases (R), and
deceased cases (D) as follows [10, 11]:
Ndt
= − IS
dS þ (1)
dt N
= IS − (yR + yD)I
dI þ (2)
dt R
dR
= y I
(3)
dt D
dD
= y I
(4)
Initial total population (N) is assumed to be constant during
pandemic as follows:
N = S + R + I + D = cons. (5)
In the above equations, the transmission rate (þ) shows
growth of an infected epidemic. The recovery rate (yR) shows
growth of recovered cases and the death rate (yD) indicates
deceased cases during a pandemic. The removing rate
(y = y + y ) expresses recovered and deceased populationsR D
removed from susceptible population. Another important factor
is called the reproduction number (RO = þ⁄y) dictating
outbreak of an endemic. If RO > 1 then it is expected an
infected person comes in contact of RO susceptible people
before he/she is removed.
As observed in above equations, if the solution to equation (2)
on infected population is known, then we can easily solve
recovered and deceased equations (3) and (4). Below, an
analytical solution based on Weibull distribution function is
introduced.
B. Weibull-SIRD Model
The most commonly used Weibull distribution function of two
parameter family (k, c) may be reformulated for infected
population of a pandemic as follows [12]:
t k
I(t) = N (
k
) (
t
)
k–1
exe [− ( ) ] (6)
c c c
In equation (6), I(t) is the Weibull function of daily
infected population, N is the total susceptible population, k is a
unitless shape factor and c is a constant time on unit of (day),
usually referred as scale factor. The values of N, k, and c are
model parameters and are obtained by fitting Weibull function
to infectious population (I) from a pandemic data.
Exact solutions to recovered (R) and deceased (D) is simply
obtained by plugging equation (6) into equations (3) and (4) to
obtain cumulative solution as follows [12].
t k
R(t) = yR ƒ I(t)dt = yRN [1 − exe (− (c
) )] (7)
D D
t
c
k
D(t) = y ƒ I(t)dt = y N [1 − exe (− ( ) )] (8)
Substituting equation (6) into equation (1), one may obtain a
solution for susceptible population as follows.
ln (
S
) = ƒ
dS
= −
þ
ƒ I(t)dt = −þ [1 − exe (− (
t
)
k
)]S0 S N c
(10)
t k
S = SOexe {−þ [1 − exe (− (c
) )]} (11)
By changing the total susceptible population (N) in SIRD
model, the recovered and deceased will be massively changed.
However, in Weibull-SIRD model, we should stick to a fixed
number for N to best fit infected cases with Weibull function in
equation (6). To fine-tune the expected recovered and deceased
cases, we propose to use variable recovery rate ( yR ) and
deceased rate (yD ) as follows.
c
k
yR = yRO [1 − exe (− (
t
) )]
n – 1
(12)
t k n –1
yD = yDO [1 − exe (− (c
) )] (13)
The power factor (n) is any number and can be adequately
fine-tuned to best fit the recovered and deceased populations
data.
The above set of analytical equations (6), (7), (8), and (11)
provide a simple and robust solution to an endemic/pandemic
data. We have applied optimization to get best value of
coefficients in SIRD and Weibull-SIRD models. MATLAB
algorithm (lsqcurvefit) was applied to find best coefficients in
SIRD model equations (1) to (5). MATLAB algorithm
(fminsearch) was used to find best fit coefficients in Weibull-
SIRD model equations. The goodness of fitted COVID-19 data
are examined using the coefficient of determination (R2) [13].
III. RESULTS
Results of Weibull-SIRD analytical model are provided and
discussed for COVID-19 in Kuwait and UAE below.
A. COVID-19 Prediction inKuwait
Results of Weibull-SIRD analytical model are provided and
discussed for COVID-19 in Kuwait and UAE below.
6. Table 1: Optimized Weibull-SIRD parameters for COVID-19 in Kuwait (18 June 2020).
Total
populatio
n
(N)
shape
facto
r (k)
Scale
facto
r (c)
Growt
h rate
(þ)
Recover
y rate
(yRO)
Death
rate
(yDO)
Removin
g rate (yO)
Reproductio
n number
(RO)
R2(S) R2(I) R2(R) R2(D)
555,509 7.1 98.97 0.0786 0.0686 0.0008 0.02719 1.13 0.985 0.975 0.949 0.719
3 5 5 3
Figure 1: Daily exposure of COVID-19 pandemic in Kuwait
The results of fitting equations (6) - (13) with COVID-19
data in Kuwait are given in Table 1.
Figure 2: Weibull-SIRD model for fitting 4-set of COVID-19
data simultaneously in Kuwait; Top) Infected, recovered, and
deceased population; Bottom) Susceptible population
Figure 2 shows that 4-set of cumulative COVID-19 data
including susceptible, infected, recovered, deceased are
simultaneously fitted with Weibull-SIRD curves. Goodness of
fit (R2) values are shown in Table 1. As shown in Fig. 2, on
Sunday 31 May 2020 Kuwait had passed the peak of COVID-
19 infectious with 14,814 infected cases. Both peak dates and
values reported 10 June 2020 and 18, 431 using direct solution
of SIRD ODE equations [15]. COVID-19 data for Kuwait on
31 May 2020 suggest 15,445 infected cases; while on 10 June
2020, there was 10,260 infected cases. Weibull-SIR model
predicts 10,581 infected cases on 10 June 2020. It is obvious
from the results that the Weibull-SIR model provided closer
and robust solution to COVID-19 pandemic in Kuwait.
B. COVID-19 Prediction inUAE
Results of COVID-19 pandemic from 29 January 2020 to 31
May 2020 for 124 days are used to examine Weibull-SIR
model. Figure 3 shows daily exposure to COVID-19 in UAE
since the outbreak. Figure 4 shows Weibull-SIRD curves is
simultaneously fitted with 4-set of COVID-19 data including
susceptible, infected, recovered, deceased in UAE. Goodness
of fit (R2) values are shown in Table 2. As shown in Fig. 4,
Weibull-SIRD model predicted that on Saturday 23 May 2020
UAE had reached with the peak of COVID-19 infectious with
15,191 infected cases whilst the reported COVID-19 data was
13,769 cases on this date. The standard SIRD model has
predicted 15,607 infected cases.
7. Table 2: Optimized Weibull-SIRD parameters for COVID-19 in UAE (31 May 2020).
Total
population
(N)
shape
factor
(k)
Scale
factor
(c)
Growth
rate
(þ)
Recovery
rate
(yRO)
Death
rate
(yDO)
Removing
rate (yO)
Reproduction
number(RO)
R2(S) R2(I) R2(R) R2(D)
803,827 6.0 118.45 0.0628 0.0474 0.00085 0.02719 1.3 0.9927 0.9887 0.9862 0.7692
Figure 3: Daily exposure of COVID-19 pandemic in UAE (31
May 2020). Figure 4: Weibull-SIRD model for fitting 4-set of COVID-19
data simultaneously in UAE; Top) Infected, recovered, and
deceased population; Bottom) Susceptible population (31 May
2020).
Figure 5: Comparison of Weibull-SIRD analytical method
with SIRD ODE model for COVID-19 data in UAE (31 May
2020).
8. The results of fitting equations (6) - (13) with COVID-19 data
in UAE are given in Table 2. Figure 5 compares Weibull-SIRD
model with the standard SIRD ODE model. Both models fitted
well with recovered COVID-19 data in UAE; although,
Weibull-SIRD model seems have predicted better infected
cases than SIRD ODE model. SIRD Model predicted longer
recovery date whilst Weibull-SIRD model have predicted
shorter period. On 21 June 2020, COVID-19 data on recovered
is 31,754 cases, Weibull-SIRD predicted 35,513 and SIRD
model predicted 39,674. More data files and more numerical
studies on COVID-19 pandemic is needed to provide solid
decision but so far Weibull-SIRD model provided promising
results.
IV. CONCLUTIONS
Better predictive methods are needed to tackle contagious
diseases as early as possible. COVID-19 pandemic is a proof
that we are in continuous need of better predictive methods. In
this paper, a novel analytical model based on Weibull-SIRD
method is introduced to study endemic/pandemic data. Weibull
distribution function provides a very good probability density
function to many applications in statistics and engineering
including wind energy. Conclusions of this work may be drawn
as follows:
• We successfully applied SIRD model to fit COVID-19 data
simultaneously for infected (I), recovered (R), and deceased
(D) and suggest important peak dates and numbers of exposed
populations.
• The new Weibull-SIRD model uses very simple and robust
analytical formulations and fit well with COVID-19 data and is
optimized for calculating model parameters.
• We studied COVID-19 data for Kuwait and UAE using both
Weibull-SIRD analytical method and SIRD ODE method.
• The peak of infectious curve for COVID-19 is predicted
around Sunday 31 May 2020 in Kuwait with 14,814 active
infected cases.
• The peak of infectious curve for COVID-19 is predicted
around Saturday 23 May 2020 in UAE with 15,191 infected
cases; although, actual peak is observed on 4 June 2020 with
17,173 infected cases.
Weibull-SIRD model is a new and promising predictive
method proposed here for studying endemic/pandemic
outbreaks. Further works still needed to better understand all
merits and features of the new Weibull-SIRD method.
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