Abstract
The purpose of this work is to investigate the almost surely exponentially stable of a stochastic SIS model with double epidemic hypothesis and specific nonlinear incidence rate. We establish the global existence and positivity of solution. Furthermore, the stability of the disease-free equilibrium of the model are showed. The analytical results are illustrated by computer simulations.
Highlights
Epidemiology is the study of the spread of diseases with the objective to trace factors that are responsible for or contribute to their occurrence
The authors of [6, 7, 8] investigated the epidemic model with double epidemic hypothesis which has two epidemic diseases caused by two different viruses
We consider a deterministic SI model with double epidemic hypothesis and cure rate described by the following differential system r2) I2, where S(t) represents the number of susceptibles at time t, I1 and I2 are the total population of the infectives with virus V1 and V2 at time t, respectively
Summary
Epidemiology is the study of the spread of diseases with the objective to trace factors that are responsible for or contribute to their occurrence It has been investigated by several mathematicians through establishing mathematical models for a long time We consider a deterministic SI model with double epidemic hypothesis and cure rate described by the following differential system. The incidence rate of disease Ii is modeled by the specifc functional response βiSIi/1 + αiS + γiIi + μiSIi, where αi, γi, μi ≥ 0. Namely, βidt is replaced by βidt + σidBi(t), where Bi independent standard Brownian motions and σi represent the intensities of the white noises of Bi. the corresponding stochastic system to (1) can be STABILITY ANALYSIS OF A STOCHASTIC SIS MODEL WITH DOUBLE EPIDEMIC HYPOTHESIS ... We close the paper with discussions and future directions
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