A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching. (English) Zbl 1492.92093
Summary: In this paper, the stochastic SIS epidemic model with vaccination under regime switching is further investigated. A new threshold \(R^s_0\) which is different from that given in [X. Zhang et al., Appl. Math. Lett. 59, 87–93 (2016; Zbl 1343.60095)] is established. A new technique to deal with the nonlinear incidence and vaccination for stochastic epidemic model under regime switching is proposed. When \(R^s_0>0\), the existence of a unique stationary distribution and the ergodic property are obtained by constructing a new stochastic Lyapunov function with Markov switching. The corresponding result which is acquired in [loc. cit.] is improved and extended.
MSC:
| 92D30 | Epidemiology |
| 92C60 | Medical epidemiology |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
stochastic SIS epidemic model; stationary distribution; Markov switching; threshold; nonlinear incidence; vaccinationCitations:
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