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Stochastic SIRS model under regime switching. (English) Zbl 1267.34079
The authors develop a stochastic SIRS model under regime switching, which includes terms representing white and color noise. It is shown that under some conditions, a solution of the corresponding system of stochastic equations remains positive and does not explode with probability one. It is also shown that the disease-free equilibrium of the model is stochastically asymptotically stable and the model is stochastically ultimately bounded. To prove their results, the authors construct several Lyapunov functions.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34D20 Stability of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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