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Stochastic models of some endemic infections. (English) Zbl 0991.92026
Summary: Stochastic models are established and studied for several endemic infections with demography. Approximations of quasi-stationary distributions and of times to extinction are derived for stochastic versions of SI, SIS, SIR, and SIRS models. The approximations are valid for sufficiently large population sizes. Conditions for validity of the approximations are given for each of the models. These are also conditions for validity of the corresponding deterministic models. It is noted that some deterministic models are unacceptable approximations of the stochastic models for a large range of realistic parameter values.
MSC:
92D30Epidemiology
60J70Applications of Brownian motions and diffusion theory