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A stochastic model of AIDS and condom use. (English) Zbl 1101.92037
Summary: We introduce stochasticity into a model of AIDS and condom use via the technique of parameter perturbation which is standard in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as desired in any population dynamics. We also carry out a detailed analysis on asymptotic stability both in probability one and in p th moment. Our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system.

MSC:
92D30 Epidemiology
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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