Approximating time to extinction for endemic infection models

Damian Clancy, Elliott Tjia

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Abstract

Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterise their performance in terms of simplicity, accuracy, and generality. To this end, we consider first the classic stochastic susceptible-infected-susceptible (SIS) model, and then a multi-dimensional generalisation of this which allows for Erlang distributed infectious periods. We find that (i) for a below-threshold infection initiated by a small number of infected individuals, approximation via a linear branching process works well; (ii) for an above-threshold infection initiated at endemic equilibrium, methods from Hamiltonian statistical mechanics yield correct asymptotic behaviour as population size becomes large; (iii) the widely-used Ornstein-Uhlenbeck diffusion approximation gives a very poor approximation, but may retain some value for qualitative comparisons in certain cases; (iv) a more detailed diffusion approximation can give good numerical approximation in certain circumstances, but does not provide correct large population asymptotic behaviour, and cannot be relied upon without some form of external validation (eg simulation studies).
Original languageEnglish
Pages (from-to)1043–1067
Number of pages25
JournalMethodology and Computing in Applied Probability
Volume20
Issue number4
Early online date24 Feb 2018
DOIs
Publication statusPublished - Dec 2018

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