title: The effect of waning immunity on long-term behaviour of stochastic models for the spread of infection.
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.
authors: Department of Mathematical Sciences, University of Liverpool, Liverpool, UK. d.clancy@liv.ac.uk
authors: Damian
authors: D
authors: Clancy
authors: Sang Taphou
authors: ST
authors: Mendy
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000276:immunology*; D003198:Computer Simulation; D004196:Disease Outbreaks; D006801:Humans; D008390:Markov Chains; D018448:Models, Immunological; D017711:Nonlinear Dynamics; D015995:Prevalence