Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate

Qun Liu, Daqing Jiang, Tasawar Hayat and Ahmed Alsaedi

Physica A: Statistical Mechanics and its Applications, 2019, vol. 521, issue C, 614-625

Abstract: In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic reproduction number R0S which can be regarded as a threshold to use in identifying the stochastic extinction and persistence: if R0S<1, the disease dies out exponentially with probability one; while if R0S>1, there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease.

Keywords: Extinction; Stationary distribution and ergodicity; Markov switching; Ratio-dependent incidence rate; Threshold (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:521:y:2019:i:c:p:614-625

DOI: 10.1016/j.physa.2019.01.115

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