Applied Mathematics & Information Sciences

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This paper aims to study the dynamic behavior of a stochastic SIS (Susceptible-Infected-Susceptible) epidemic model with varying population size and constant flow of new members of whom a specified fraction is infective. First, we show that the solution is stochastically ultimately bounded and permanent. Then, we investigate the persistence in the mean of the variable I(t) (the number of infected members). Next, we use the Markov semigroups theory to investigate the ergodicity of the solution. Mainly, we show that a stationary distribution for the solution always exists for all values of the parameters in this model. Finally, Numerical simulations are carried out to illustrate the theoretical results.

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