Stochastic and deterministic models for SIS epidemics among a population partitioned into households.
Models for the spread of an SIS epidemic among a population consisting of m households, each containing n individuals, are considered and their behaviour is analysed under the practically relevant situation when m is large and n small. A threshold parameter R* is determined. For the stochastic model it is shown that the epidemic has a non-zero probability of taking off if and only if R* > 1, and the extension to unequal household sizes is also considered. For the deterministic model, with households of size 2, it is shown that if R* < or = 1 then the epidemic dies out, whilst if R* > 1 the epidemic settles down to an endemic equilibrium. The usual basic reproductive ratio R0 does not provide a good indicator for the behaviour of these household epidemic models unless the household size n is large.
Ball
F
F
Department of Mathematical Sciences, University of Nottingham, University Park, UK. frank.ball@maths.nott.ac.uk
D019353:Endemic Diseases; D004813:Epidemiology; D006801:Humans; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D016012:Poisson Distribution; D013269:Stochastic Processes