Qualitative study of a stochastic SIS epidemic model with vertical transmission. (English) Zbl 1514.92176
Summary: In this paper, we study a stochastic SIS epidemic model with vertical infection. By constructing suitable stochastic Lyapunov function, we establish sufficient conditions for the existence of a stationary probability measure of the model. In addition, we also establish sufficient conditions for extinction and persistence of the disease.
MSC:
| 92D30 | Epidemiology |
| 34F05 | Ordinary differential equations and systems with randomness |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60J28 | Applications of continuous-time Markov processes on discrete state spaces |
Keywords:
stochastic random; epidemic model; vertical transmission; stationary distribution; extinction; persistenceReferences:
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