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Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response

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  • Mouhcine Naim
  • Fouad Lahmidi

Abstract

The purpose of this paper is to investigate the stability of a deterministic and stochastic SIS epidemic model with double epidemic hypothesis and specific nonlinear incidence rate. We prove the local asymptotic stability of the equilibria of the deterministic model. Moreover, by constructing a suitable Lyapunov function, we obtain a sufficient condition for the global stability of the disease-free equilibrium. For the stochastic model, we establish global existence and positivity of the solution. Thereafter, stochastic stability of the disease-free equilibrium in almost sure exponential and th moment exponential is investigated. Finally, numerical examples are presented.

Suggested Citation

  • Mouhcine Naim & Fouad Lahmidi, 2020. "Analysis of a Deterministic and a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis and Specific Functional Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-11, May.
    • Handle: RePEc:hin:jnddns:5362716
    DOI: 10.1155/2020/5362716
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