The asymptotic behavior of a stochastic multigroup SIS model. (English) Zbl 1387.34074
Summary: In this paper, we explore the long time behavior of a multigroup susceptible-infected-susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 34F05 | Ordinary differential equations and systems with randomness |
| 34E10 | Perturbations, asymptotics of solutions to ordinary differential equations |
| 92D30 | Epidemiology |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
Keywords:
multigroup susceptible-infected-susceptible (SIS) model; disease free equilibrium; endemic equilibrium; exponential stability; prevail; stationary distributionReferences:
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