DOCSLIB.ORG

Some Mathematical Models in Epidemiology

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis Some Mathematical Models in Epidemiology by Peeyush Chandra Department of Mathematics and Statistics Indian Institute of Technology Kanpur, 208016 Email: [email protected] Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis Definition (Epidemiology) It is a discipline, which deals with the study of infectious diseases in a population. It is concerned with all aspects of epidemic, e.g. spread, control, vaccination strategy etc. WHY Mathematical Models ? The aim of epidemic modeling is to understand and if possible control the spread of the disease. In this context following questions may arise: • How fast the disease spreads ? • How much of the total population is infected or will be infected ? • Control measures ! • Effects of Migration/ Environment/ Ecology, etc. • Persistence of the disease. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis Infectious diseases are basically of two types: Acute (Fast Infectious): • Stay for a short period (days/weeks) e.g. Influenza, Chickenpox etc. Chronic Infectious Disease: • Stay for larger period (month/year) e.g. hepatitis. In general the spread of an infectious disease depends upon: • Susceptible population, • Infective population, • The immune class, and • The mode of transmission. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis Assumptions We shall make some general assumptions, which are common to all the models and then look at some simple models before taking specific problems. • The disease is transmitted by contact (direct or indirect) between an infected individual and a susceptible individual. • There is no latent period for the disease, i.e., the disease is transmitted instantaneously when the contact takes place. • All susceptible individuals are equally susceptible and all infected ones are equally infectious. • The population size is large enough to take care of the fluctuations in the spread of the disease, so a deterministic model is considered. • The population, under consideration is closed, i.e. has a fixed size. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis • X (t)- population of susceptible, Y (t)- population of infected ones. • If B is the average contact number with susceptible which leads to new infection per unit time per infective, then Y (t + ∆t) = Y (t) + BY (t)∆t dY which in the limit ∆t ! 0 gives dt = BY (t). S-I Model • It is observed that B depends upon the susceptible population. So, define β = average number of contact between susceptible and infective which leads to new infection per unit time per susceptible per infective, then B = βX (t), which gives, dY = βX (t)Y (t) = β(N − Y )Y : dt where N = X + Y is the total population, which is fixed as per the above assumption. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis • Pathogen causes illness for a period of time followed by immunity. S(Susseptible) −! I (Infected) • S: Previously unexposed to the pathogen. • I: Currently colonized by pathogen. • Proportion of populations: S = X =N; I = Y =N: • We ignore demography of population (death/birth & migration). Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis SIS (No Immunity) [Ross, 1916 for Malaria] 1 • Recovery rate α Infectious period is taken to be constant though infection period (the time spent in the infectious class) is distributed about a mean value & can be estimated from the clinical data. In the above model, it is assumed that the whole population is divided into two classes susceptible and infective; and that if one is infected then it remains in that class. However, this is not the case, as an infected person may recover from the disease. • If γ is the rate of recovery from infective class to susceptible class, then dS dt = γI − βSI ; dI (3) dt = βSI − γI ; dI 1 β = β 1 − − I I ; R0 = : dt R0 γ S∗ = 1 and I ∗ = 1 − 1 , feasible if R > 1. R0 R0 0 Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis SIR Model (Kermack & McKendrick 1927) • Pathogen causes illness for a period of time followed by immunity. S(Susseptible) −! I (Infected) −! R(Recovered) • S: Previously unexposed to the pathogen. • I: Currently colonized by pathogen. • R: Successfully cleared from the infection. • Proportion of populations: S = X =N; I = Y =N; R = Z=N: • We ignore demography of population (death/birth & migration). Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis In view of the above assumption the SIR model is given by 8 dS = −βSI ; > dt > < dI dt = βSI − γI ; (4) > > :> dR dt = γI ; with initial conditions: S(0) > 0; I (0) > 0 & R(0) = 0. 1 • γ : Average infectious period. γ dI • Note that if S(0) < β , then initially dt < 0 and the infection dies out. • Threshold phenomenon. γ γ • Thus, for an infection to invade, S(0) > β or if β : removal rate is small enough then the disease will spread. • The inverse of removal rate is defined as 'basic reproductive γ ratio' R0 = β . Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis Basic Reproduction Ratio It is defined as the average number of secondary cases arising from an average primary case in an entirely susceptible population i.e. the rate at which new infections are produces by an infectious individual in an entirely susceptible population. • It measures the maximum reproductive potential for an infectious disease. • If S(0) = 1, then disease will spread if R0 > 1. If the disease is transmitted to more than one host then it will spread. • R0 depends on disease and host population e.g. ◦ R0 = 2:6 for TB in cattle. ◦ R0 = 3 − 4 for Influenza in humans. ◦ R0 = 3:5 − 6 for small pox in humans. ◦ R0 = 16 − 18 for Measles in humans. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis Note 1 • For an infectious disease with an average infectious period γ and β transmission rate β, R0 = γ . • For a closed population, infection with specified R0, can invade only if threshold fraction of susceptible population is greater than 1 . R0 • Vaccination can be used to reduce the susceptible population below 1 . R0 Also we see that dS = −R S ) S(t) = S(0)e−R0R(t): dR 0 • This implies as the epidemic builds up S(t) # and so R(t) ". • There will always be same susceptible in the population as S(t) > 0. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis • The epidemic breaks down when I = 0, we can say S(1) = 1 − R(1) = S(0)e−R0R(1): or 1 − R(1) − S(0)e−R0R(1) = 0: (5) • R1 is the final proportion of individuals recovered = total number of infected proportion. • We can assume that for given S(0) > R0; the equation (2) has a roots between 0 & 1. −R0 [R1 = 0 ) 1 − S0 > 0 and R1 = 1 ) −S(0)e < 0]: • dR = γ(1 − S − R) = γ[1 − S(0)e−R0R − R]: dt • Solve it (i) Numerically. (ii) For small R0R, i.e. when R0 << 1 or at the start of the epidemic. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis SIR model with demography Assumptions • Population size does not change - good in developed countries. • New born are with passive immunity and hence susceptible. • This is good enough if the average age at which immunity is lost << typical age of infection.(e.g. in developed countries t1 = 6 months << t2 = 4 − 5 years.) • Vertical transmission is ignored. 8 dS dt = ν − βSI − µS; < dI dt = βSI − γI − µI ; (6) : dR dt = γI − µR; Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis 1 • µ is the rate at which individual suffer natural mortality i.e. µ is natural host life span. β • R0 = γ+µ : 1 • γ+µ is the average time which an individual spends in each class. Equilibrium States (i) (S; I ; R) = (1; 0; 0), disease free. (ii) (S∗; I ∗; R∗) = ( 1 ; µ (R − 1); (1 − 1 )(1 − µ )), for µ < γ. R0 β 0 R0 γ • Clearly, R0 > 1 for endemic equilibrium. • It can be seen that endemic equilibrium is stable if R0 > 1, otherwise disease free equilibrium is stable. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis • The characteristic equation for Jacobian at endemic equilibrium 2 (λ + µ)[λ + µR0λ + (µ + γ)µ(R0 − 1)] = 0: (7) q 2 4 −µR µR0 − AG λ = −µ and λ = 0 ± ; 1 2;3 2 2 where, A = 1 , denotes mean age of infection. µ(R0−1) 1 G = µ+γ : typical period of infectivity. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis SIRS (Waning Immunity) 8 dS dt = ν + !R − βSI − µS; < dI dt = βSI − (γ + µ)I ; (8) : dR dt = γI − µR − !R; ! : the rate at which immunity is lost. β R = : 0 γ + µ SEIR Model Transmission of disease starts with a low number of pathogen (bacterial cells etc.) which reproduce rapidly within host. • At this time the pathogen is present in host but can not transmit disease to other susceptible. Peeyush Chandra Some Mathematical Models in Epidemiology Preliminary Definitions and Assumptions Mathematical Models and their analysis • Infected but not infectious ) E class.
Load more

Recommended publications
  • Continuous Time Individual-Level Models of Infectious Disease: Epiilmct
    Continuous Time Individual-Level Models of Infectious Disease: EpiILMCT Waleed Almutiry Vineetha Warriyar K V Rob Deardon Qassim University Uinversity of Calgary University of Calgary Abstract This paper describes the R package EpiILMCT, which allows users to study the spread of infectious disease using continuous time individual level models (ILMs). The package provides tools for simulation from continuous time ILMs that are based on either spatial demographic, contact network, or a combination of both of them, and for the graphical summarization of epidemics. Model fitting is carried out within a Bayesian Markov Chain Monte Carlo (MCMC) framework. The continuous time ILMs can be implemented within either susceptible-infected-removed (SIR) or susceptible- infected-notified-removed (SINR) compartmental frameworks. As infectious disease data is often partially observed, data uncertainties in the form of missing infection times - and in some situations missing removal times - are accounted for using data augmentation techniques. The package is illustrated using both simulated and an experimental data set on the spread of the tomato spotted wilt virus (TSWV) disease. Keywords: EpiILMCT, infectious disease, individual level modelling, spatial models, con- tact networks, R. 1. Introduction Innovative mathematical and mechanistic approaches to the modelling of infectious dis- eases are continuing to emerge in the literature. These can be used to understand the spread of disease through a population - whether homogeneous or heterogeneous - and enable researchers to construct predictive models to develop control strategies to disrupt arXiv:2006.00135v1 [stat.AP] 30 May 2020 disease transmission. For example, Deardon et al. (2010) introduced a class of discrete time individual-level models (ILMs) which incorporate population heterogeneities by modelling the transmission of disease given various individual-level risk factors.
    [Show full text]
  • The Basic Reproduction Number As a Predictor for Epidemic Outbreaks in Temporal Networks
    The basic reproduction number as a predictor for epidemic outbreaks in temporal networks Petter Holme1,2,3 and Naoki Masuda4 1Department of Energy Science, Sungkyunkwan University, 440-746 Suwon, Korea 2IceLab, Department of Physics, Umeå University, 90187 Umeå, Sweden 3Department of Sociology, Stockholm University, 10961 Stockholm, Sweden 4Department of Engineering Mathematics, University of Bristol, BS8 1UB, Bristol, UK E-mail address: [email protected] Abstract The basic reproduction number R₀—the number of individuals directly infected by an infectious person in an otherwise susceptible population—is arguably the most widely used estimator of how severe an epidemic outbreak can be. This severity can be more directly measured as the fraction people infected once the outbreak is over, Ω. In traditional mathematical epidemiology and common formulations of static network epidemiology, there is a deterministic relationship between R₀ and Ω. However, if one considers disease spreading on a temporal contact network—where one knows when contacts happen, not only between whom—then larger R₀ does not necessarily imply larger Ω. In this paper, we numerically investigate the relationship between R₀ and Ω for a set of empirical temporal networks of human contacts. Among 31 explanatory descriptors of temporal network structure, we identify those that make R₀ an imperfect predictor of Ω. We find that descriptors related to both temporal and topological aspects affect the relationship between R₀ and Ω, but in different ways. Introduction The interaction between medical and theoretical epidemiology of infectious diseases is probably not as strong as it should. Many results in the respective fields fail to migrate to the other.
    [Show full text]
  • Epidemic Models
    Chapter 9 Epidemic Models 9.1 Introduction to Epidemic Models Communicable diseases such as measles, influenza, and tuberculosis are a fact of life. We will be concerned with both epidemics, which are sudden outbreaks of a disease, and endemic situations, in which a disease is always present. The AIDS epidemic, the recent SARS epidemic, recurring influenza pandemics, and outbursts of diseases such as the Ebola virus are events of concern and interest to many peo- ple. The prevalence and effects of many diseases in less-developed countries are probably not as well known but may be of even more importance. Every year mil- lions, of people die of measles, respiratory infections, diarrhea, and other diseases that are easily treated and not considered dangerous in the Western world. Diseases such as malaria, typhus, cholera, schistosomiasis, and sleeping sickness are endemic in many parts of the world. The effects of high disease mortality on mean life span and of disease debilitation and mortality on the economy in afflicted countries are considerable. We give a brief introduction to the modeling of epidemics; more thorough de- scriptions may be found in such references as [Anderson & May (1991), Diekmann & Heesterbeek (2000)]. This chapter will describe models for epidemics, and the next chapter will deal with models for endemic situations, but we begin with some general ideas about disease transmission. The idea of invisible living creatures as agents of disease goes back at least to the writings of Aristotle (384 BC–322 BC). It developed as a theory in the sixteenth century. The existence of microorganisms was demonstrated by van Leeuwenhoek (1632–1723) with the aid of the first microscopes.
    [Show full text]
  • Commentary Inducing Autoimmune Disease to Treat Cancer
    Proc. Natl. Acad. Sci. USA Vol. 96, pp. 5340–5342, May 1999 Commentary Inducing autoimmune disease to treat cancer Drew M. Pardoll Department of Oncology, Johns Hopkins University School of Medicine, Baltimore, MD 21205-2196 For many years, visions for development of successful immu- colleagues (6) discovered that the target for a melanoma- notherapy of cancer revolved around the induction of immune specific CD81 T cell clone grown from a melanoma patient was responses against tumor-specific ‘‘neoantigens.’’ However, as wild-type tyrosinase, a melanosomal enzyme selectively ex- demonstrated in a recent paper in the Proceedings by Overwijk pressed in melanocytes and responsible for one of the steps in et al. (1), the generation of tissue-specific autoimmune re- melanin biosynthesis. Subsequently, a number of investigators sponses represents an approach to cancer immunotherapy that found that their melanoma-specific CD81 T cells indeed is gaining momentum. Thus, a new principle in cancer therapy recognized melanocyte-specific antigens rather than melano- states that the ability to induce tissue-specific autoimmunity ma-specific antigens (7–10). Most of these antigens appear to will allow for the treatment of many important cancers. be melanosomal proteins, and a number of them, including The original focus on tumor-specific neoantigens derived tyrosinase, TRP-1, TRP-2, and gp100, are involved in melanin from a number of findings. Vaccination-challenge experiments biosynthesis. Other melanosomal proteins such as MART1y performed between carcinogen-induced murine tumor models Melan A have no known function but are nonetheless mela- typically demonstrated that autologous tumors vaccinated nocyte-specific tissue differentiation antigens.
    [Show full text]
  • Clustering of Susceptible Individuals Within Households Can Drive an Outbreak: an Individual-Based Model Exploration
    medRxiv preprint doi: https://doi.org/10.1101/2019.12.10.19014282; this version posted December 14, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Clustering of susceptible individuals within households can drive an outbreak: an individual-based model exploration Elise Kuylen1,2,*, Lander Willem1, Jan Broeckhove3, Philippe Beutels1, and Niel Hens1,4 1Centre for Health Economics Research and Modelling Infectious Diseases (CHERMID), Vaccine and Infectious Disease Institute, University of Antwerp, Antwerp, Belgium 2Discipline Group Computer Sciences, Hasselt University, Hasselt, Belgium 3IDLab, Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium 4I-BioStat, Data Science Institute, Hasselt University, Hasselt, Belgium *[email protected] ABSTRACT When estimating important measures such as the herd immunity threshold, and the corresponding efforts required to eliminate measles, it is often assumed that susceptible individuals are uniformly distributed throughout populations. However, unvaccinated individuals may be clustered in a variety of ways, including by geographic location, by age, in schools, or in households. Here, we investigate to which extent different levels of within-household clustering of susceptible individuals may impact the risk and persistence of measles outbreaks. To this end, we apply an individual-based model, Stride, to a population of 600,000 individuals, using data from Flanders, Belgium. We compare realistic scenarios regarding the distribution of susceptible individuals within households in terms of their impact on epidemiological measures for outbreak risk and persistence.
    [Show full text]
  • Lesson 1 Introduction to Epidemiology
    Lesson 1 Introduction to Epidemiology Epidemiology is considered the basic science of public health, and with good reason. Epidemiology is: a) a quantitative basic science built on a working knowledge of probability, statistics, and sound research methods; b) a method of causal reasoning based on developing and testing hypotheses pertaining to occurrence and prevention of morbidity and mortality; and c) a tool for public health action to promote and protect the public’s health based on science, causal reasoning, and a dose of practical common sense (2). As a public health discipline, epidemiology is instilled with the spirit that epidemiologic information should be used to promote and protect the public’s health. Hence, epidemiology involves both science and public health practice. The term applied epidemiology is sometimes used to describe the application or practice of epidemiology to address public health issues. Examples of applied epidemiology include the following: • the monitoring of reports of communicable diseases in the community • the study of whether a particular dietary component influences your risk of developing cancer • evaluation of the effectiveness and impact of a cholesterol awareness program • analysis of historical trends and current data to project future public health resource needs Objectives After studying this lesson and answering the questions in the exercises, a student will be able to do the following: • Define epidemiology • Summarize the historical evolution of epidemiology • Describe the elements of a case
    [Show full text]
  • Foundations of Epidemiology
    66221_CH01_5398.qxd 6/19/09 11:16 AM Page 1 © Jones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION CHAPTER 1 Foundations of Epidemiology OBJECTIVES After completing this chapter, you will be able to: ■ Define epidemiology. ■ Define descriptive epidemiology. ■ Define analytic epidemiology. ■ Identify some activities performed in epidemiology. ■ Explain the role of epidemiology in public health practice and individual decision making. ■ Define epidemic, endemic, and pandemic. ■ Describe common source, propagated, and mixed epidemics. ■ Describe why a standard case definition and adequate levels of reporting are important in epidemiologic investigations. ■ Describe the epidemiology triangle for infectious disease. ■ Describe the advanced epidemiology triangle for chronic diseases and behavioral disorders. ■ Define the three levels of prevention used in public health and epidemiology. ■ Understand the basic vocabulary used in epidemiology. 66221_CH01_5398.qxd 6/19/09 11:16 AM Page 2 © Jones and Bartlett Publishers, LLC. NOT FOR SALE OR DISTRIBUTION 2 CHAPTER 1 ■ Foundations of Epidemiology In recent years, the important role of epidemiology has become increasingly recognized. Epidemiology is a core subject required in public health and health education programs; it is a study that provides information about public health problems and the causes of those problems. This information is then used to improve the health and social conditions of people. Epidemiology has a population focus in that epidemiologic investigations are concerned with the collective health of the people in a community or population under study. In contrast, a clinician is concerned for the health of an individual. The clinician focuses on treating and caring for the patient, whereas the epidemiologist focuses on iden- tifying the source or exposure of disease, disability or death, the number of persons exposed, and the potential for further spread.
    [Show full text]
  • Population Dynamics of Infectious Diseases: a Discrete Time Model
    ecological modelling 198 (2006) 183–194 available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/ecolmodel Population dynamics of infectious diseases: A discrete time model Madan K. Oli a,∗, Meenakshi Venkataraman a, Paul A. Klein b, Lori D. Wendland c, Mary B. Brown c a Department of Wildlife Ecology and Conservation, 110 Newins-Zeigler Hall, University of Florida, Gainesville, FL 32611-0430, United States b Department of Pathology, Immunology, and Laboratory Medicine, College of Medicine, University of Florida, Gainesville, FL 32610-0275 c Department of Infectious Diseases and Pathology, College of Veterinary Medicine, University of Florida, Gainesville, FL 32610-0880, United States article info abstract Article history: Mathematical models of infectious diseases can provide important insight into our under- Received 23 June 2005 standing of epidemiological processes, the course of infection within a host, the transmis- Received in revised form 31 March sion dynamics in a host population, and formulation or implementation of infection control 2006 programs. We present a framework for modeling the dynamics of infectious diseases in dis- Accepted 18 April 2006 crete time, based on the theory of matrix population models. The modeling framework Published on line 14 June 2006 presented here can be used to model any infectious disease of humans or wildlife with dis- crete disease states, irrespective of the number of disease states. The model allows rigorous Keywords: estimation of important quantities, including the basic reproduction ratio of the disease Basic reproduction ratio R0 (R0) and growth rate of the population ( ), and permits quantification of the sensitivity of R0 Epidemiological model and to model parameters.
    [Show full text]
  • Into to Epidemic Modeling
    INTRO TO EPIDEMIC MODELING Introduction to epidemic modeling is usually made through one of the first epidemic models proposed by Kermack and McKendrick in 1927, a model known as the SIR epidemic model When a disease spreads in a population it splits the population into nonintersecting classes. In one of the simplest scenarios there are 3 classes: • The class of individuals who are healthy but can contract the disease. These people are called susceptible individuals or susceptibles. The size of this class is usually denoted by S. • The class of individuals who have contracted the disease and are now sick with it, called infected individuals. In this model it is assumed that infected individuals are also infectious. The size of the class of infectious/infected individuals is denoted by I. • The class of individuals who have recovered and cannot contract the disease again are called removed/recovered individuals. The class of recovered individuals is usually denoted by R. The number of individuals in each of these classes changes with time, that is, S(t), I(t), and R(t). The total population size N is the sum of these three classes 푁 푡 = 푆 푡 + 퐼 푡 + 푅(푡) Assumptions: (1) Infected individuals are also infectious; (2) The total population size remains constant; (3) The population is closed (no immigration/emigration); (4) No births/deaths; (5)All recovered individuals have complete immunity Epidemiological models consist of systems of ODEs which describe the dynamics in each class. To derive the differential equations, we consider how the classes change in time. When a susceptible individual enters into a contact with an infectious individual, that susceptible individual becomes infected and moves from the susceptible class into the infected class.
    [Show full text]
  • Nber Working Paper Series Vaccine Hesitancy
    NBER WORKING PAPER SERIES VACCINE HESITANCY, PASSPORTS AND THE DEMAND FOR VACCINATION Joshua S. Gans Working Paper 29075 http://www.nber.org/papers/w29075 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 July 2021 Thanks to Ajay Agrawal, Avi Goldfarb and Richard Holden for helpful discussions. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2021 by Joshua S. Gans. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Vaccine Hesitancy, Passports and the Demand for Vaccination Joshua S. Gans NBER Working Paper No. 29075 July 2021 JEL No. I12,I18 ABSTRACT Vaccine hesitancy is modelled as an endogenous decision within a behavioural SIR model with endogenous agent activity. It is shown that policy interventions that directly target costs associated with vaccine adoption may counter vaccine hesitancy while those that manipulate the utility of unvaccinated agents will either lead to the same or lower rates of vaccine adoption. This latter effect arises with vaccine passports whose effects are mitigated in equilibrium by reductions in viral/disease prevalence that themselves reduce the demand for vaccination. Joshua S. Gans Rotman School of Management University of Toronto 105 St. George Street Toronto ON M5S 3E6 CANADA and NBER [email protected] 1 Introduction Vaccine hesitancy, whereby individuals elect not to be vaccinated, has been a long-standing issue in public health.
    [Show full text]
  • The Quantitative Genetics of the Endemic Prevalence of Infectious Diseases: Indirect Genetic Effects Dominate Heritable Variation and Response to Selection
    bioRxiv preprint doi: https://doi.org/10.1101/2021.04.07.438789; this version posted April 9, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC-ND 4.0 International license. The quantitative genetics of the endemic prevalence of infectious diseases: Indirect Genetic Effects dominate heritable variation and response to selection Piter Bijma1, Andries Hulst1,2, Mart C. M. de Jong2 1Animal Breeding and Genomics, Wageningen University and Research, Wageningen, the Netherlands 2Quantitative Veterinary Epidemiology, Wageningen University and Research, Wageningen, the Netherlands Abstract Pathogens have profound effects on life on earth, both in nature and agriculture. Despite the availability of well-established epidemiological theory, however, a quantitative genetic theory of the host population for the endemic prevalence of infectious diseases is almost entirely lacking. While several studies have demonstrated the relevance of the transmission dynamics of infectious diseases for heritable variation and response to selection of the host population, our current theoretical framework of quantitative genetics does not include these dynamics. As a consequence, we do not know which genetic effects of the host population determine the prevalence of an infectious disease, and have no concepts of breeding value and heritable variation for endemic prevalence. Here we propose a quantitative genetic theory for the endemic prevalence of infectious diseases. We first identify the genetic factors that determine the prevalence of an infectious disease, using an approach founded in epidemiological theory. Subsequently we investigate the population level effects of individual genetic variation on 푅0 and on the endemic prevalence.
    [Show full text]
  • An S-I-S Model of Streptococcal Disease with a Class of Beta-Hemolytic Carriers BU-1524-M
    An S-I-S Model of Streptococcal Disease with a Class of Beta-Hemolytic Carriers BU-1524-M Kevin Doura Howard University Julio D. Melendez-Morales University of Puerto Rico, Humacao Gigi G. Meyer Virginia Polytechnic Institute and State University Luis E. Perez University of California, Irvine November 23,2000 Abstract We analyzed the dynamics of an epidemic in a population infected with Streptococcal pyogenes (S. pyogenes), the causative agent in strep throat, with a Susceptible-Injected-Susceptible (S-I-S) model that in­ cludes an extra class of infectious carriers. Our model represents a three dimensional nonlinear differential equation system, which de­ scribes the spread of the disease in a population with three epidemi­ ological classes: susceptible (S), infected (I) and beta-hemolytic car­ riers (C). We focus on the impact that the classes I and C have on S, and the rate at which groups move in and out of the infectious state. Lastly, we study the long-term dynamics of the disease in the population. 493 1 Introduction Humans are a natural reservoir for the beta-hemolytic group A Streptococ­ cus; transmission from person to person is frequently associated with an asymptomatic carrier who is colonized in the nasopharynx [10]. An asymp­ tomatic carrier is one who carries the infection but does not develop the symptoms of the infection.Streptococcaceae is a family made up of gram pos­ itive bacteria: round cocci that usually grow in chains of various lengths. Consisting of A, B, C, D, ... ,V groups, of these A, Band D are of great­ est pathogenic significance.
    [Show full text]