See also:
- https://food4innovations.blog/2020/03/26/montecarlo-simulaties-tonen-aan-wat-de-onzekerheid-is-en-dat-we-minimaal-1600-maar-misschien-wel-2000-2500-ic-plaatsen-nodig-hebben/
Madhav Marathe and Anil Vullikanti will present a tutorial on computational epidemiology, along with Thomas L. Phillips Professor of Engineering Naren Ramakrishnan, at the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining on August 24th, 2014 in New York City.
In this tutorial, the researchers will approach epidemics based on diffusion processes on complex networks, which are able to capture more realistic problems. They will provide a state of the art overview of computational epidemiology, a multi-disciplinary research area that overlaps different areas in computer science, including data mining, machine learning, high performance computing and theoretical computer science, as well as mathematics, economics and statistics.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Madhav Marathe and Anil Vullikanti will present a tutorial on computational epidemiology, along with Thomas L. Phillips Professor of Engineering Naren Ramakrishnan, at the 20th ACM SIGKDD Conference on Knowledge Discovery and Data Mining on August 24th, 2014 in New York City.
In this tutorial, the researchers will approach epidemics based on diffusion processes on complex networks, which are able to capture more realistic problems. They will provide a state of the art overview of computational epidemiology, a multi-disciplinary research area that overlaps different areas in computer science, including data mining, machine learning, high performance computing and theoretical computer science, as well as mathematics, economics and statistics.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Measles, Vaccines, Antibodies and Big Pharma Money
Did you know that the AMA strongly discourages ANY comments by Medical Professionals that cast any doubt on the efficacy of vaccines? Did you also know there are several studies that show vaccines as being ineffective and that the basis of vaccines (formation of antibodies to speed up the immune response) has been shown to be invalid? Learn the truth here. Oh, by the way, no vaccine manufacturer can be held liable for any negative side-effects of their products.
++++++++++++++++++++++++++++++++++++++++++
At http://bergmanchiropractic.com and http://Owners-Guide.com we strive to educate people on natural solutions to health.
-------------------------------------------------------------------------------------
http://www.theArthritisReversalSystem.com is my online video course with 21 videos, 3 manuals and an online forum!
++++++++++++++++++++++++++++++++++++++++++
https://www.owners-guide.com/online-consultation/ for online consults.
_________________________________________________
SUBSCRIBE at http://www.youtube.com/user/johnbchiro
CALL TOLL FREE 1-855-712-0012 to get bonus materials not on YouTube or text your first name and email plus 89869 to 1-817-591-2905.
Economic analysis of malaria burden in kenyaNanyingi Mark
This framework uses a cost of illness approach to evaluate the burden of malaria. The evaluation is based on private direct costs (PDC) and private indirect cost (PIC) of malaria attack per episode.
The SIR Model and the 2014 Ebola Virus Disease Outbreak in Guinea, Liberia an...CSCJournals
This research presents a mathematical model aimed at understanding the spread of the 2014 Ebola Virus Disease (EVD) using the standard SIR model. In modelling infectious disease dynamics, it is necessary to investigate whether the disease spread could attain an epidemic level or it could be wiped out. Data from the 2014 Ebola Virus Disease outbreak is used and Guinea where the outbreak started is considered in this study. A three dimensional non-linear differential equation is formulated and solved numerically using the Runge-Kutta 4th order method in the Vensim Personal Learning Edition Software. It is shown from the study that, with public health interventions, the effective reproductive number can be reduced making it possible for the outbreak to die out. It is also shown mathematically that the epidemic can only die out when there are no new infected individuals in the population.
Towards a malaria-free world - Background informationXplore Health
This guide provides background information on malaria, the most important parasitic disease in the world. Explore all aspects of malaria from the causes to treatment. Investigate the latest research and uncover the ethical, legal and social issues surrounding this disease.
Measles, Vaccines, Antibodies and Big Pharma Money
Did you know that the AMA strongly discourages ANY comments by Medical Professionals that cast any doubt on the efficacy of vaccines? Did you also know there are several studies that show vaccines as being ineffective and that the basis of vaccines (formation of antibodies to speed up the immune response) has been shown to be invalid? Learn the truth here. Oh, by the way, no vaccine manufacturer can be held liable for any negative side-effects of their products.
++++++++++++++++++++++++++++++++++++++++++
At http://bergmanchiropractic.com and http://Owners-Guide.com we strive to educate people on natural solutions to health.
-------------------------------------------------------------------------------------
http://www.theArthritisReversalSystem.com is my online video course with 21 videos, 3 manuals and an online forum!
++++++++++++++++++++++++++++++++++++++++++
https://www.owners-guide.com/online-consultation/ for online consults.
_________________________________________________
SUBSCRIBE at http://www.youtube.com/user/johnbchiro
CALL TOLL FREE 1-855-712-0012 to get bonus materials not on YouTube or text your first name and email plus 89869 to 1-817-591-2905.
Economic analysis of malaria burden in kenyaNanyingi Mark
This framework uses a cost of illness approach to evaluate the burden of malaria. The evaluation is based on private direct costs (PDC) and private indirect cost (PIC) of malaria attack per episode.
The SIR Model and the 2014 Ebola Virus Disease Outbreak in Guinea, Liberia an...CSCJournals
This research presents a mathematical model aimed at understanding the spread of the 2014 Ebola Virus Disease (EVD) using the standard SIR model. In modelling infectious disease dynamics, it is necessary to investigate whether the disease spread could attain an epidemic level or it could be wiped out. Data from the 2014 Ebola Virus Disease outbreak is used and Guinea where the outbreak started is considered in this study. A three dimensional non-linear differential equation is formulated and solved numerically using the Runge-Kutta 4th order method in the Vensim Personal Learning Edition Software. It is shown from the study that, with public health interventions, the effective reproductive number can be reduced making it possible for the outbreak to die out. It is also shown mathematically that the epidemic can only die out when there are no new infected individuals in the population.
Towards a malaria-free world - Background informationXplore Health
This guide provides background information on malaria, the most important parasitic disease in the world. Explore all aspects of malaria from the causes to treatment. Investigate the latest research and uncover the ethical, legal and social issues surrounding this disease.
Surveillance of healthcare-associated infections: understanding and utilizing...Evangelos Kritsotakis
Presented at the EUCIC Basic Module for Infection Prevention and Control, Groningen, May 2022.
This module is organised by the European Committee on Infection Control (EUCIC) is taught face-to-face by top experts from different academic centres in Europe, who cover all major aspects of Infection Prevention and Control in the hospital.
Modeling the Effect of Variation of Recruitment Rate on the Transmission Dyna...IOSR Journals
In this Paper, the effect of the variation of recruitment rate on the transmission dynamics of
tuberculosis was studied by modifying an existing model. While the recruitment rate into the susceptible class of
the existing model is constant, in our modified model we used a varying recruitment rate. The models were
analyzed analytically and numerically and these results were compared. The Disease Free Equilibrium (DFE)
state of the existing model was found to be
,0,0,0
, the DFE of the modified model was found to be
( ,0,0,0) * S where * S is arbitrary. While all the eigenvalue of the existing model are negative, one of the
eigenvalues of the modified model is zero. The basic reproduction number o R of both models are established to
be the same. The numerical experiments show a gradual decline in the infected and exposed populations as the
recruitment rates increase in both models but the decline is more in the modified model than in the existing
model. This implies that eradication will be achieved faster using the model with a varying recruitment rate.
Stikstof beleid in NL v1 - Food4Innovations.pdfWouter de Heij
Voorstel:
- Ga terug naar emissie beperking.
- Stop met gebruik Aerius in wetgeving/vergunning aanvragen.
- Deel Nederland op in regios.
- Ontkoppel NOx met Ammoniak
- Kom met duidelijke concrete maatregelen.
Almost 80 years old, and therefore long retired. My father - Harrie de Heij - is one of the designers of southern Flevoland and Almere. It was 'his project' all his life. Recently also a short interview: https://youtu.be/lDK53MunI-I
I became an entrepreneur. The agreement? Making something from nothing. Draw stripes on a blank sheet of paper and then get to work. That binds us.
Also see: https://food4innovations.blog
De duivel in ons politieke systeem - Wouter de Heij over modellen (Foodlog)Wouter de Heij
See full discussion:
https://www.foodlog.nl/artikel/modellen-zijn-de-duivel-in-ons-politieke-systeem/
and future articles on:
https://food4innovations.blog
10 vragen en antwoorden over Methaan, een kort levend broeikasgas (WUR).Wouter de Heij
Meer over herkauwers en methaan:
https://food4innovations.blog/2022/08/08/de-methaan-emissie-van-koeien-is-onderdeel-van-de-korte-c-cyclus-en-dus-niet-te-vergelijken-met-de-verbranding-van-aardgas-steenkolen-of-aardolie-dat-in-de-lange-cyclus-zit-an-inconvenient-truth/
Methaan balans:
https://food4innovations.blog/2017/07/04/de-vergroening-van-ons-energiesysteem-nodig-absoluut-maar-wat-is-nu-wijsheid-1x-de-methaan-balans/
En recente literatuur:
https://aleph-2020.blogspot.com/2019/06/greenhouse-gas-emissions.html
More fuel for the food-feed debate (FAO , 2022)Wouter de Heij
See also:
https://www.foodlog.nl/artikel//twee-gebieden-en-twee-gedachten-over-eiwitproductie-voor-mensen/allcomments/#comment-323767
And
https://www.food4innovations.blog
See also:
https://www.foodlog.nl/artikel//twee-gebieden-en-twee-gedachten-over-eiwitproductie-voor-mensen/allcomments/#comment-323727
and www.food4innovations.blog
COVID Risico's : basis achtergrond en over besmet en besmettelijkWouter de Heij
Achtergrondslides over corona, uitleg over hoe je een risico-analyse uitvoert en toelichting op besmet zijn, en besmettelijkheid en antwoord op de vraag waarom antigeen testen wel zinvol zijn.
zie ook blog-post:
zie ook:
www.food4innovations.blog
www.top-bv.nl
www.boxnb.nl
The Future of Food in het aankomende post-covid tijdperk (December 2020)Wouter de Heij
Live luisteren en vragen stellen op:
https://www.youtube.com/watch?v=gqi7unhcUOs&fbclid=IwAR11ejphFvR2dLpqbizwX0_erHfK-g82IkYsix-ve0gOPCh3QUvy0yBvzfI
Zie ook de drie afzonderlijke delen van deze keynote op YouTube:
Part1: https://youtu.be/XbPxPChzLQc
Part2: https://youtu.be/rx5tNFcC1Qw
Part3: https://youtu.be/adUvFNycHc0
Meer weten?
www.top-bv.nl
www.boxnv.nl
www.food4innovations.blog
of stuur een mail naar info@top-bv.nl
See also:
https://food4innovations.blog/2020/03/16/live-blog-over-de-corona-crisis-covid-19-dagelijkse-beschouwingen-van-wouter-de-heij-food4innovations/
and
https://food4innovations.blog/2020/03/22/corona-covid-19-en-andere-virussen-kanaal-op-youtube-food4innovations/
See also:
https://food4innovations.blog/2020/03/16/live-blog-over-de-corona-crisis-covid-19-dagelijkse-beschouwingen-van-wouter-de-heij-food4innovations/
and
https://food4innovations.blog/2020/03/22/corona-covid-19-en-andere-virussen-kanaal-op-youtube-food4innovations/
See also:
https://food4innovations.blog/2020/03/16/live-blog-over-de-corona-crisis-covid-19-dagelijkse-beschouwingen-van-wouter-de-heij-food4innovations/
and
https://food4innovations.blog/2020/03/22/corona-covid-19-en-andere-virussen-kanaal-op-youtube-food4innovations/
Demographic science aids in understanding the spread and fatality rates of CO...Wouter de Heij
See also:
https://osf.io/fd4rh/?view_only=c2f00dfe3677493faa421fc2ea38e295
and live-blog:
https://food4innovations.blog/2020/03/16/live-blog-over-de-corona-crisis-covid-19-dagelijkse-beschouwingen-van-wouter-de-heij-food4innovations/
Infectious disease modelling - the math behind CoronaWouter de Heij
See. also live blog at:
https://food4innovations.blog/2020/03/16/live-blog-over-de-corona-crisis-covid-19-dagelijkse-beschouwingen-van-wouter-de-heij-food4innovations/
Rapport monitoring leveringszekerheid 2017 TENNETWouter de Heij
Zie ook Food4Innovations.blog voor discussie over elektriciteit in Nederland en wat dit betekent voor huishoudens: https://food4innovations.blog/2020/01/19/elektrische-rijden-ik-zat-iets-verkeerd-maar-maarten-steinbuch-was-wel-erg-optimistisch-denk-ik/
Acute scrotum is a general term referring to an emergency condition affecting the contents or the wall of the scrotum.
There are a number of conditions that present acutely, predominantly with pain and/or swelling
A careful and detailed history and examination, and in some cases, investigations allow differentiation between these diagnoses. A prompt diagnosis is essential as the patient may require urgent surgical intervention
Testicular torsion refers to twisting of the spermatic cord, causing ischaemia of the testicle.
Testicular torsion results from inadequate fixation of the testis to the tunica vaginalis producing ischemia from reduced arterial inflow and venous outflow obstruction.
The prevalence of testicular torsion in adult patients hospitalized with acute scrotal pain is approximately 25 to 50 percent
Knee anatomy and clinical tests 2024.pdfvimalpl1234
This includes all relevant anatomy and clinical tests compiled from standard textbooks, Campbell,netter etc..It is comprehensive and best suited for orthopaedicians and orthopaedic residents.
- Video recording of this lecture in English language: https://youtu.be/lK81BzxMqdo
- Video recording of this lecture in Arabic language: https://youtu.be/Ve4P0COk9OI
- 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
Tom Selleck Health: A Comprehensive Look at the Iconic Actor’s Wellness Journeygreendigital
Tom Selleck, an enduring figure in Hollywood. has captivated audiences for decades with his rugged charm, iconic moustache. and memorable roles in television and film. From his breakout role as Thomas Magnum in Magnum P.I. to his current portrayal of Frank Reagan in Blue Bloods. Selleck's career has spanned over 50 years. But beyond his professional achievements. fans have often been curious about Tom Selleck Health. especially as he has aged in the public eye.
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Introduction
Many have been interested in Tom Selleck health. not only because of his enduring presence on screen but also because of the challenges. and lifestyle choices he has faced and made over the years. This article delves into the various aspects of Tom Selleck health. exploring his fitness regimen, diet, mental health. and the challenges he has encountered as he ages. We'll look at how he maintains his well-being. the health issues he has faced, and his approach to ageing .
Early Life and Career
Childhood and Athletic Beginnings
Tom Selleck was born on January 29, 1945, in Detroit, Michigan, and grew up in Sherman Oaks, California. From an early age, he was involved in sports, particularly basketball. which played a significant role in his physical development. His athletic pursuits continued into college. where he attended the University of Southern California (USC) on a basketball scholarship. This early involvement in sports laid a strong foundation for his physical health and disciplined lifestyle.
Transition to Acting
Selleck's transition from an athlete to an actor came with its physical demands. His first significant role in "Magnum P.I." required him to perform various stunts and maintain a fit appearance. This role, which he played from 1980 to 1988. necessitated a rigorous fitness routine to meet the show's demands. setting the stage for his long-term commitment to health and wellness.
Fitness Regimen
Workout Routine
Tom Selleck health and fitness regimen has evolved. adapting to his changing roles and age. During his "Magnum, P.I." days. Selleck's workouts were intense and focused on building and maintaining muscle mass. His routine included weightlifting, cardiovascular exercises. and specific training for the stunts he performed on the show.
Selleck adjusted his fitness routine as he aged to suit his body's needs. Today, his workouts focus on maintaining flexibility, strength, and cardiovascular health. He incorporates low-impact exercises such as swimming, walking, and light weightlifting. This balanced approach helps him stay fit without putting undue strain on his joints and muscles.
Importance of Flexibility and Mobility
In recent years, Selleck has emphasized the importance of flexibility and mobility in his fitness regimen. Understanding the natural decline in muscle mass and joint flexibility with age. he includes stretching and yoga in his routine. These practices help prevent injuries, improve posture, and maintain mobilit
These lecture slides, by Dr Sidra Arshad, offer a quick overview of physiological basis of a normal electrocardiogram.
Learning objectives:
1. Define an electrocardiogram (ECG) and electrocardiography
2. Describe how dipoles generated by the heart produce the waveforms of the ECG
3. Describe the components of a normal electrocardiogram of a typical bipolar leads (limb II)
4. Differentiate between intervals and segments
5. Enlist some common indications for obtaining an ECG
Study Resources:
1. Chapter 11, Guyton and Hall Textbook of Medical Physiology, 14th edition
2. Chapter 9, Human Physiology - From Cells to Systems, Lauralee Sherwood, 9th edition
3. Chapter 29, Ganong’s Review of Medical Physiology, 26th edition
4. Electrocardiogram, StatPearls - https://www.ncbi.nlm.nih.gov/books/NBK549803/
5. ECG in Medical Practice by ABM Abdullah, 4th edition
6. ECG Basics, http://www.nataliescasebook.com/tag/e-c-g-basics
Report Back from SGO 2024: What’s the Latest in Cervical Cancer?bkling
Are you curious about what’s new in cervical cancer research or unsure what the findings mean? Join Dr. Emily Ko, a gynecologic oncologist at Penn Medicine, to learn about the latest updates from the Society of Gynecologic Oncology (SGO) 2024 Annual Meeting on Women’s Cancer. Dr. Ko will discuss what the research presented at the conference means for you and answer your questions about the new developments.
Pulmonary Thromboembolism - etilogy, types, medical- Surgical and nursing man...VarunMahajani
Disruption of blood supply to lung alveoli due to blockage of one or more pulmonary blood vessels is called as Pulmonary thromboembolism. In this presentation we will discuss its causes, types and its management in depth.
Title: Sense of Taste
Presenter: Dr. Faiza, Assistant Professor of Physiology
Qualifications:
MBBS (Best Graduate, AIMC Lahore)
FCPS Physiology
ICMT, CHPE, DHPE (STMU)
MPH (GC University, Faisalabad)
MBA (Virtual University of Pakistan)
Learning Objectives:
Describe the structure and function of taste buds.
Describe the relationship between the taste threshold and taste index of common substances.
Explain the chemical basis and signal transduction of taste perception for each type of primary taste sensation.
Recognize different abnormalities of taste perception and their causes.
Key Topics:
Significance of Taste Sensation:
Differentiation between pleasant and harmful food
Influence on behavior
Selection of food based on metabolic needs
Receptors of Taste:
Taste buds on the tongue
Influence of sense of smell, texture of food, and pain stimulation (e.g., by pepper)
Primary and Secondary Taste Sensations:
Primary taste sensations: Sweet, Sour, Salty, Bitter, Umami
Chemical basis and signal transduction mechanisms for each taste
Taste Threshold and Index:
Taste threshold values for Sweet (sucrose), Salty (NaCl), Sour (HCl), and Bitter (Quinine)
Taste index relationship: Inversely proportional to taste threshold
Taste Blindness:
Inability to taste certain substances, particularly thiourea compounds
Example: Phenylthiocarbamide
Structure and Function of Taste Buds:
Composition: Epithelial cells, Sustentacular/Supporting cells, Taste cells, Basal cells
Features: Taste pores, Taste hairs/microvilli, and Taste nerve fibers
Location of Taste Buds:
Found in papillae of the tongue (Fungiform, Circumvallate, Foliate)
Also present on the palate, tonsillar pillars, epiglottis, and proximal esophagus
Mechanism of Taste Stimulation:
Interaction of taste substances with receptors on microvilli
Signal transduction pathways for Umami, Sweet, Bitter, Sour, and Salty tastes
Taste Sensitivity and Adaptation:
Decrease in sensitivity with age
Rapid adaptation of taste sensation
Role of Saliva in Taste:
Dissolution of tastants to reach receptors
Washing away the stimulus
Taste Preferences and Aversions:
Mechanisms behind taste preference and aversion
Influence of receptors and neural pathways
Impact of Sensory Nerve Damage:
Degeneration of taste buds if the sensory nerve fiber is cut
Abnormalities of Taste Detection:
Conditions: Ageusia, Hypogeusia, Dysgeusia (parageusia)
Causes: Nerve damage, neurological disorders, infections, poor oral hygiene, adverse drug effects, deficiencies, aging, tobacco use, altered neurotransmitter levels
Neurotransmitters and Taste Threshold:
Effects of serotonin (5-HT) and norepinephrine (NE) on taste sensitivity
Supertasters:
25% of the population with heightened sensitivity to taste, especially bitterness
Increased number of fungiform papillae
263778731218 Abortion Clinic /Pills In Harare ,sisternakatoto
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The prostate is an exocrine gland of the male mammalian reproductive system
It is a walnut-sized gland that forms part of the male reproductive system and is located in front of the rectum and just below the urinary bladder
Function is to store and secrete a clear, slightly alkaline fluid that constitutes 10-30% of the volume of the seminal fluid that along with the spermatozoa, constitutes semen
A healthy human prostate measures (4cm-vertical, by 3cm-horizontal, 2cm ant-post ).
It surrounds the urethra just below the urinary bladder. It has anterior, median, posterior and two lateral lobes
It’s work is regulated by androgens which are responsible for male sex characteristics
Generalised disease of the prostate due to hormonal derangement which leads to non malignant enlargement of the gland (increase in the number of epithelial cells and stromal tissue)to cause compression of the urethra leading to symptoms (LUTS
NVBDCP.pptx Nation vector borne disease control programSapna Thakur
NVBDCP was launched in 2003-2004 . Vector-Borne Disease: Disease that results from an infection transmitted to humans and other animals by blood-feeding arthropods, such as mosquitoes, ticks, and fleas. Examples of vector-borne diseases include Dengue fever, West Nile Virus, Lyme disease, and malaria.
Dynamics and Control of Infectious Diseases (2007) - Alexander Glaser
1. Dynamics and
Control of Infectious
Diseases
Alexander Glaser
WWS556d
Princeton University
April 9, 2007
Revision 3
1
2. Definitions
Infectious Disease
About a quarter of all deaths worldwide are due to infectious diseases
(about 60% are due to non-communicable conditions)
An infectious disease is contagious if it is easily transmitted (from person to person)
Disease caused by invasion of the body by an agent
Pathogen, i.e. a microparasite that causes disease, e.g. a virus or bacterium
Agent
Agent may be transmitted by a vector (droplet, mosquito, etc.)
Vector
2
3. • Incubation (latent) period
• Prodromal (initial, pre-eruptive) period
• Overtly symptomatic (infectious) period
• Recovery period (no longer infectious)
Stages of an Infectious Disease
(generic)
Depending on the disease, a person may or may not be able
to transmit the disease during incubation and prodromal periods
Relative infectiousness in the prodromal and the symptomatic
periods determine the optimal control strategy
3
4. Definitions
Epidemic
Outbreak of an infectious disease affecting
a disproportionately large number of individuals in a population,
community, or region within a short period of time
Pandemic
Spread of an epidemic to a large region (or worldwide)
An infectious disease is endemic when it is maintained in a
population without the need for external inputs
Endemic
4
5. Transmission Factor R0
(of the microparasite, also: basic reproduction number)
Infected primary individual is placed in a large susceptible population
R0: average number of secondary individuals infected by one primary case
(applicable in the early stages of an epidemic)
Reff = R0(1 − p)Effective transmission factor (if a fraction p is immune):
Reff < 1 −→ p > 1 −
1
R0
Critical fraction of the population that has to be immune to prevent epidemic
EpidemicR0 > 1 EndemicR0 = 1 EradicationR0 < 1
5
6. Typical Transmission Factors
Smallpox 3-5 70-80%
Measles 10-20 90-95%
Malaria (100)* 99%
Infectious Disease R0 p(min)
*Malaria needs specific “external” vector (mosquito) for transmission
Current level of U.S. population immune against smallpox: about 18%
(growth rate of epidemic today would be much higher than those of historical smallpox epidemics)
6
7. Why Mathematical Modeling?
Mathematical modeling is typically the only way to
examine the possible impact of different release and control scenarios
STRENGTHS AND BENEFITS
Questions that can be addressed:
What fraction of the population should be quarantined and/or vaccinated?
How fast have control measures to be implemented?, etc.
Several important aspects of epidemics are difficult to quantify
(e.g. response of population to certain events)
PROBLEMS
Simple models cannot capture the complexity of epidemics and their dynamics
Complex models are intransparent and difficult to validate
7
8. Dynamics of Infectious Diseases
Basic Model
based on
R. M. Anderson and R. M. May
Infectious Diseases of Humans: Dynamics and Control
Oxford University Press, 1991
8
9. Assumptions and Simplifications
(incomplete list)
Three groups: susceptible X(t), infectious Y(t), and recovering (immune) Z(t)
No age-dependency of variables and parameters
No incubation period (only one “infectious” group)
Total population constant (no deaths caused by disease): N = X(t) + Y(t) + Z(t)
Constant mortality rate (“Type II survival”)
All susceptibles are equally at risk of infection (“weak homogeneous mixing”)
All births into the susceptible class
9
12. Time [years]
Fractionofpopulation[%]
0 20 40 60 80 100
0
0.2
0.4
0.6
0.8
1.0
Epidemic and Endemic Phases
(of an infectious disease)
infectious
For very large times, a constant fraction
of about 0.1% of the population infectious
12
16. Response Options to an Outbreak
and the Potential Role of Mathematical Modeling
to Identify Optimal Control Strategies
Smallpox
16
17. About Smallpox
Lethality: about 30% (depending on many factors, some types > 98%)
Long incubation period: about 2-3 weeks (possibility of localized control measures)
Once endemic in humans; eradicated in 1979, primarily by mass vaccination
Humans are (or have been) only known host of virus
Agent: variola virus
Mode of transmission: infective droplets via face-to-face contact
17
18. About Smallpox
Vaccination may have severe side effects
Mass vaccination campaign likely to cause more deaths
than locally isolated smallpox epidemic
Temporary retention of samples (officially) in only two locations today
Centers for Disease Control and Prevention, Atlanta, Georgia, United States of America (about 400 strains)
Russian State Centre for Research on Virology and Biotechnology, Koltsovo, Novosibirsk Region, Russian Federation (about 120 strains)
Destruction of samples originally scheduled for June 30, 1999
1947 smallpox incident in New York City
one infectious person traveling to the city by bus from Mexico
mass vaccination of several million people
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20. Outbreak Control Options
BENEFITS DRAWBACKS
Minimizes use of vaccine
Contacts need to be found at an early
stage of incubation
Highly effective during eradication
campaign (with background levels of
herd immunity high)
Less effective in “mobile” society
Effective at stopping widespread
dissemination; not dependent on
contact tracing
Large numbers have to be vaccinated
quickly; unnecessary morbidity
and mortality
Useful for protecting first-responders;
if used for entire population, no need
for rapid implementation
If used for entire population, high
long-term costs and (unnecessary)
morbidity and mortality
Isolation and quarantine
Movement restrictions
Ring vaccination
Targeted (“local mass”) vaccination
Mass vaccination
Prophylactic vaccination
CONTAINMENTVACCINATION
Potentially useful in containing
a small outbreak
Difficult to police, compromised by any
“illegal” movements, coercive
Highly effective at reducing
transmission from known cases
Needs adequate facilities; compulsory
policy coercive; requires rapid
detection of cases
Adapted from N. M. Ferguson et al., Planning for Smallpox Outbreaks, Nature, Vol. 425, October 2003
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21. Modeling Complexity
Source: Ferguson et al., Nature (425), 2003
Deterministic models
Solve equations (fast), “hopefully” capture the average epidemic behavior
Stochastic models
Simulation (slow), recognize random nature of transmission events (important in early/late stages of epidemic)
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22. Advanced Methods: Example 1
(Deterministic Model)
S. Del Valle et al.,
Effects of behavioral changes in a smallpox attack model,
Mathematical Biosciences 195 (2005)
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23. a high percentage (2.3% per day)
of people reduce their daily number
of contacts by a factor of 10
S. Del Valle et al., Mathematical Biosciences 195 (2005)
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24. S. Del Valle et al., Mathematical Biosciences 195 (2005)
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26. Covert smallpox attack on a generic city (attack site is university in city center)
EpiSimS
Los Alamos National Laboratory
Computer and Computational Sciences Division (CCS)
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28. Concluding Remarks
Modeling can be a useful tool to identify a “credible” set of control options
and to assess their relative effectiveness under certain conditions
In the event of an outbreak of an infectious disease:
Real-time data collection and modeling
How much information would be available in the early stages of an epidemic?
(potentially insufficient to “feed” the available models adequately)
There are no “single most efficient” response strategies
Modeling can also suggest certain trigger thresholds, i.e. when to escalate responses
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29. References
• R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control,
Oxford University Press, 1991
• N. M. Ferguson et al., Planning for Smallpox Outbreaks, Nature, Vol. 425, October 2003,
pp. 681-685
• S. Del Valle, H. Hethcote, J.M. Hyman, and C. Castillo-Chavez, Effects of Behavioral
Changes in a Smallpox Attack model, Mathematical Biosciences, 195 (2005), pp. 228-251
• R. N. Nelson, Mathematical Models of Smallpox Epidemic, WWS556d Lecture Slides, 2003
• Centers for Disease Control and Prevention, http://www.bt.cdc.gov/agent/smallpox/
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