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 pth moment exponential is investigated. Finally, numerical examples are presented.
Highlights
Epidemiology is the study of the spread of infectious diseases with the objective to trace factors that are responsible for or contribute to their occurrence
The authors of [6,7,8,9] investigated the epidemic model SIS with double epidemic hypothesis which has two epidemic diseases caused by two different viruses
We consider a deterministic SIS model with double epidemic hypothesis described by the following differential system: Discrete Dynamics in Nature and Society
Summary
Epidemiology is the study of the spread of infectious diseases with the objective to trace factors that are responsible for or contribute to their occurrence. The susceptible individuals can be infected with only a disease. We consider a deterministic SIS model with double epidemic hypothesis described by the following differential system: Discrete Dynamics in Nature and Society. E incidence rate of disease is modeled by the specific functional response βiSIi/(1 + αiS + ciIi + μiSIi), where αi, ci, μi are saturation factors measuring the psychological or inhibitory effect.
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