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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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Stochastic modeling: The impact of chance

Stochastic modeling: The impact of chance

Chapter:
(p.45) Chapter Three Stochastic modeling: The impact of chance
Source:
Mathematical Tools for Understanding Infectious Disease Dynamics
Author(s):

Odo Diekmann

Hans Heesterbeek

Tom Britton

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691155395.003.0003

This chapter defines a stochastic counterpart to the homogeneous deterministic epidemic model introduced in Chapter 1. The model considers a homogeneous community of individuals that mix uniformly, meaning that there is no social structure in the community. The word “mix” is used in the sense of engaging in a type of contact that may possibly lead to transmission; what mixing is will therefore depend on characteristics of the infectious agent and the host. The randomness in the model stems from the latency and infectious periods being random (i.e., typically different for different individuals), and also from the contact process: infectious contacts of infected individuals occur randomly in time and with randomly selected individuals in a finite population. The chapter highlights two special cases, called the “general” epidemic and the Reed–Frost epidemic in the literature.

Keywords:   infectious disease, stochastic epidemic model, general epidemic, Reed–Frost epidemic, homogeneous community

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