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Mathematical Tools for Understanding Infectious Disease Dynamics$
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Odo Diekmann, Hans Heesterbeek, and Tom Britton

Print publication date: 2012

Print ISBN-13: 9780691155395

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691155395.001.0001

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The epidemic in a closed population

The epidemic in a closed population

Chapter:
(p.3) Chapter One The epidemic in a closed population
Source:
Mathematical Tools for Understanding Infectious Disease Dynamics
Author(s):

Odo Diekmann

Hans Heesterbeek

Tom Britton

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691155395.003.0001

This chapter discusses the case of an epidemic in a closed population. “Closed” means that demographic turnover, emigration, and immigration are not considered. The following questions may be asked: Does this cause an epidemic? If so, at what rate does the number of infected hosts increase during the rise of the epidemic? What proportion of the population will ultimately have experienced infection? We assume that we are dealing with microparasites, which are characterized by the fact that a single infection triggers an autonomous process in the host. We further assume that this process results in either death or lifelong immunity, so that no individual can be infected twice. In order to answer these questions, we first have to formulate assumptions about transmission. It is then helpful to follow a three-step procedure: model the contact process; model the mixing of susceptible and infective (i.e., infectious) individuals; and specify the probability that a contact between an infective and a susceptible actually leads to transmission.

Keywords:   infectious disease, disease transmission, epidemic, microparasites, closed population, infected host

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