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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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    3. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    4. B. B. Mukhopadhyay & P. K. Tapaswi, 1994. "An SIRS epidemic model of Japanese Encephalitis," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-9, January.
    5. Khasminskii, R.Z. & Zhu, C. & Yin, G., 2007. "Stability of regime-switching diffusions," Stochastic Processes and their Applications, Elsevier, vol. 117(8), pages 1037-1051, August.
    6. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar & Alsaedi, Ahmed, 2017. "Stationary distribution and extinction of a stochastic SIRS epidemic model with standard incidence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 510-517.
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