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

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  • Liu, Qun
  • Jiang, Daqing
  • Hayat, Tasawar
  • Alsaedi, Ahmed

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.

Suggested Citation

  • Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2019. "Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 614-625.
    • Handle: RePEc:eee:phsmap:v:521:y:2019:i:c:p:614-625
    DOI: 10.1016/j.physa.2019.01.115
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    References listed on IDEAS

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    5. Carol Y. Lin, 2008. "Modeling Infectious Diseases in Humans and Animals by KEELING, M. J. and ROHANI, P," Biometrics, The International Biometric Society, vol. 64(3), pages 993-993, September.
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