Author: Lan, Guijie; Lin, Ziyan; Wei, Chunjin; Zhang, Shuwen
Title: A stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching Cord-id: yjodgy2v Document date: 2019_9_13
ID: yjodgy2v
Snippet: In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number [Formula: see text] is established: the disease can be eradicated almost surely if [Formula: see text] and under mild extra conditions, whereas if [Form
Document: In this paper, we propose and discuss a stochastic SIRS epidemic model with non-monotone incidence rate under regime-switching. First of all, we show that there is a unique positive solution, which is a prerequisite for analyzing the long-term behavior of the stochastic model. Then, a threshold dynamic determined by the basic reproduction number [Formula: see text] is established: the disease can be eradicated almost surely if [Formula: see text] and under mild extra conditions, whereas if [Formula: see text] the densities of the distributions of the solution can converge in L(1) to an invariant density by using the Markov semigroups theory. Finally, based on realistic parameters obtained from previous literatures, numerical simulations have been performed to verify our analytical results.
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