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Stochastic permanence of an epidemic model with a saturated incidence rate

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  • Hussain, Ghulam
  • Khan, Amir
  • Zahri, Mostafa
  • Zaman, Gul

Abstract

We study a stochastic model with a generalized (saturated) incidence. The random perturbations are assumed to be dependent on white noises. This implies that the random perturbation will be proportional directly to the steady states. We then show the existence as well as the uniqueness of the solution with the help of constructing a Lyapunov function. We will also discuss the bounded-ness and stochastic permanence for our proposed model with sufficient conditions. The numerical simulations are carried out using first-order Itô-Taylor stochastic scheme to demonstrate the obtained results.

Suggested Citation

  • Hussain, Ghulam & Khan, Amir & Zahri, Mostafa & Zaman, Gul, 2020. "Stochastic permanence of an epidemic model with a saturated incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304033
    DOI: 10.1016/j.chaos.2020.110005
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    References listed on IDEAS

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    Cited by:

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    3. 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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