Persistence time of SIS infections in heterogeneous populations and networks

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Abstract

For a susceptible–infectious–susceptible infection model in a heterogeneous population, we present simple formulae giving the leading-order asymptotic (large population) behaviour of the mean persistence time, from an endemic state to extinction of infection. Our model may be interpreted as describing an infection spreading through either (1) a population with heterogeneity in individuals’ susceptibility and/or infectiousness; or (2) a heterogeneous directed network. Using our asymptotic formulae, we show that such heterogeneity can only reduce (to leading order) the mean persistence time compared to a corresponding homogeneous population, and that the greater the degree of heterogeneity, the more quickly infection will die out.
Original languageEnglish
Pages (from-to)545-570
Number of pages26
JournalJournal of Mathematical Biology
Volume77
Issue number3
Early online date23 Feb 2018
DOIs
Publication statusPublished - Sep 2018

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