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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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Other indicators of severity

Other indicators of severity

(p.205) Chapter Eight Other indicators of severity
Mathematical Tools for Understanding Infectious Disease Dynamics

Odo Diekmann

Hans Heesterbeek

Tom Britton

Princeton University Press

This chapter is devoted to the initial real-time growth rate r, the probability of a major outbreak, the final size, and the endemic level, in structured populations, with special attention for computational simplifications in the case of separable mixing. Chapter 7 studied the basic reproduction number R₀ for epidemic models in populations manifesting various forms of heterogeneity. It was illustrated that R₀ depends on the transmission parameters, contact rates, the infectious period and on the community structure. The importance of R₀ lies in the fact that an epidemic can, and will in the deterministic setting, take off only if R₀ > 1, a characteristic referred to as supercritical. In a community having births or immigration of susceptibles, this also means that the disease can become endemic. If the parameters and community are such that R₀ < 1 (or R₀ = 1), we are in the subcritical (critical) regime and an epidemic outbreak cannot occur. The chapter examines important supplementary characteristic features and shows how they depend on the different parameters of the model.

Keywords:   infectious disease, disease outbreaks, reproduction number, growth rate, separable mixing, epidemic outbreak

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