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1. Generating Function and Invasion Probability with a Fixed Duration of Infection
BibTeX
@MISC{Lloyd_1.generating,
author = {L. Lloyd and Ji Zhang and A. Morgan Root},
title = {1. Generating Function and Invasion Probability with a Fixed Duration of Infection},
year = {}
}
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Abstract
Assuming that the duration of infection is fixed leads to a Poisson distribution for the secondary infections. Such a Poisson distribution has generating function given by G(s) = exp(µ(s − 1)) (Grimmett and Stirzaker, 1992), where µ is the mean number of secondary infections. In the setting of a directly transmitted infection, equation (3.1) of the main text can be used to find the probability of extinction for the branching process, starting with one infectious individual, which (as it is throughout this paper) is written as s. This gives the transcendental equation s = exp{R0(s − 1)}. (A.1) As usual, s is the smallest non-negative solution of this equation. The probability of a major outbreak is then given by 1 − s. In the branching process description of the well-mixed host-vector model, the number of secondary infections amongst vectors (respectively hosts) due to an infec-tive host (respectively vector) is Poisson distributed, with mean RHV0 (respectively RV H0) (Diekmann and Heesterbeek, 2000). Thus an equation of the form s = exp
Keyphrases
invasion probability fixed duration secondary infection poisson distribution non-negative solution main text well-mixed host-vector model rv h0 form exp transcendental equation exp r0 infectious individual branching process mean rhv0 infec-tive host branching process description mean number major outbreak
