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

Mouhcine Naim and Fouad Lahmidi

Discrete Dynamics in Nature and Society, 2020, vol. 2020, 1-11

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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:5362716

DOI: 10.1155/2020/5362716

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