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A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

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  • Settati, A.
  • Lahrouz, A.
  • Zahri, M.
  • Tridane, A.
  • El Fatini, M.
  • El Mahjour, H.
  • Seaid, M.

Abstract

This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold Rs(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when Rs(g)=1. Numerical illustrations of the findings are given via different types of function g.

Suggested Citation

  • Settati, A. & Lahrouz, A. & Zahri, M. & Tridane, A. & El Fatini, M. & El Mahjour, H. & Seaid, M., 2021. "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000436
    DOI: 10.1016/j.chaos.2021.110690
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    1. Saha, Pritam & Mondal, Bapin & Ghosh, Uttam, 2023. "Dynamical behaviors of an epidemic model with partial immunity having nonlinear incidence and saturated treatment in deterministic and stochastic environments," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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