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Stochastic Epidemic Models in Structured Populations Featuring Dynamic Vaccination and Isolation

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Frank Ball ,
Philip D. O'Neill  and
James Pike
Frank Ball*
Affiliation:
University of Nottingham
Philip D. O'Neill*
Affiliation:
University of Nottingham
James Pike*
Affiliation:
University of Nottingham
*
∗Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
∗Postal address: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
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Abstract

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We consider a stochastic model for the spread of an SEIR (susceptible → exposed → infective → removed) epidemic among a population of individuals partitioned into households. The model incorporates both vaccination and isolation in response to the detection of cases. When the infectious period is exponential, we derive an explicit formula for a threshold parameter, and analytic results that enable computation of the probability of the epidemic taking off. These quantities are found to be independent of the exposure period distribution. An approximation for the expected final size of an epidemic that takes off is obtained, evaluated numerically, and found to be reasonably accurate in large populations. When the infectious period is not exponential, but has an increasing hazard rate, we obtain stochastic comparison results in the case where the exposure period is fixed. Our main result shows that as the exposure period increases, both the severity of the epidemic in a single household and the threshold parameter decrease, under certain assumptions concerning isolation. Corresponding results for infectious periods with decreasing hazard rates are also derived.

Keywords

Epidemicstochastic epidemicvaccinationbioterrorismcouplingfinal outcome

MSC classification

Secondary: 92D30: Epidemiology 60K99: None of the above, but in this section
Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 3 , September 2007 , pp. 571 - 585
Copyright
Copyright © Applied Probability Trust 2007 

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