The effect of waning immunity on long-term behaviour of stochastic models for the spread of infection.

Journal of Mathematical Biology
Damian Clancy, Sang Taphou Mendy

Abstract

In stochastic modelling of infectious spread, it is often assumed that infection confers permanent immunity, a susceptible-infective-removed (SIR) model. We show how results concerning long-term (endemic) behaviour may be extended to a susceptible-infective-removed-susceptible (SIRS) model, in which immunity is temporary. Since the full SIRS model with demography is rather intractable, we also consider two simpler models: the susceptible-infective-susceptible (SIS) model with demography, in which there is no immunity; and the SIRS model in a closed population. For each model, we first analyse a deterministic model, then approximate the quasi-stationary distribution (equilibrium distribution conditional upon non-extinction of infection) using a moment closure technique. We look in particular at the effect of the immune period upon infection prevalence and upon time to fade-out of infection. Our main findings are that a shorter average immune period leads to higher infection prevalence in quasi-stationarity, and to longer persistence of infection in the population.

References

Apr 16, 1999·Mathematical Biosciences·I Nåsell
Mar 5, 2003·Theoretical Population Biology·Ingemar Nåsell
Sep 2, 2003·Theoretical Population Biology·Ingemar Nåsell
Jul 6, 2004·Journal of Theoretical Biology·T J HagenaarsN M Ferguson
Apr 6, 2005·Theoretical Population Biology·Ingemar Nåsell
May 17, 2005·Bulletin of Mathematical Biology·Isthrinayagy KrishnarajahGavin Gibson
Feb 16, 2007·Mathematical Biosciences·Isthrinayagy KrishnarajahGavin Gibson

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Citations

Aug 15, 2013·Bulletin of Mathematical Biology·Ingemar Nåsell
Oct 25, 2011·Theoretical Population Biology·J R Artalejo, M J Lopez-Herrero
Apr 14, 2017·Royal Society Open Science·Alberto AletaYamir Moreno
Mar 9, 2018·Royal Society Open Science·Rebecca H ChisholmNicholas Geard
Sep 4, 2012·Journal of Mathematical Biology·Damian Clancy, Christopher J Pearce

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