Periodic solution and ergodic stationary distribution of two stochastic SIQS epidemic systems

Haokun Qi, Shengqiang Zhang, Xinzhu Meng and Huanhe Dong

Physica A: Statistical Mechanics and its Applications, 2018, vol. 508, issue C, 223-241

Abstract: This paper proposes two stochastic SIQS epidemic models with periodic parameters and Markov switching. We first prove that the stochastic non-autonomous periodic system has a nontrivial positive periodic solution by using the Khasminskii’s theory. Then the sufficient conditions for extinction of the disease are obtained. Furthermore, we construct suitable stochastic Lyapunov functions with regime switching to prove the existence of ergodic stationary distribution of the stochastic SIQS epidemic model. At last, some rigorous numerical simulations are presented to illustrate our theoretical results.

Keywords: Stochastic SIQS epidemic model; Periodic solution; Stationary distribution; Extinction; Markov switching (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:508:y:2018:i:c:p:223-241

DOI: 10.1016/j.physa.2018.05.075

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