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01-Applied Mathematics & Information Sciences
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Volumes > Volume 12 > No. 6

 
   

The Effect of Immigration on The Persistence and Ergodicity of a Stochastic SIS Model for Transmission of Disease

PP: 1127-1138
doi:10.18576/amis/120607
Author(s)
Youness El Ansari, Ali El Myr, Lahcen Omari, Aadil Lahrouz,
Abstract
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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