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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 concept of state

The concept of state

Chapter:
(p.153) Chapter Six The concept of state
Source:
Mathematical Tools for Understanding Infectious Disease Dynamics
Author(s):

Odo Diekmann

Hans Heesterbeek

Tom Britton

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691155395.003.0006

This chapter considers the case of individuals who differ from each other with respect to traits that are relevant for the transmission of an infectious agent. How do we describe the spread of the agent? How do we quantify the infectivity? What happens in the initial phase? Can we characterize the final size? Examples of the “traits” we have in mind are age, sex, sexual activity level, sexual disposition, and spatial position. So a trait may be static or dynamic, it may be discrete or continuous. Traits are considered as i-states, where “i” means “individual” and where “state” signifies that the current value together with the environmental input in the intervening period completely determines future behavior. The heterogeneity of individuals is classified in terms of a component, h-state, of their i-state, while the other component, d-state, summarizes all relevant information about output of infectious material.

Keywords:   infectious disease, disease transmission, individual states, i-states, infectivity, infectious output

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