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

Authors

Youness El Ansari, Department of Mathematics, Laboratory of Computer Sciences Modeling and systems, Faculty of Sciences Dhar-Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796-Atlas, Fez, MoroccoFollow
Ali El Myr, Department of Mathematics, Laboratory of Computer Sciences Modeling and systems, Faculty of Sciences Dhar-Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796-Atlas, Fez, MoroccoFollow
Lahcen Omari, Department of Mathematics, Laboratory of Computer Sciences Modeling and systems, Faculty of Sciences Dhar-Mehraz, University Sidi Mohamed Ben Abdellah, B.P. 1796-Atlas, Fez, MoroccoFollow
Aadil Lahrouz, Department of Mathematics, Laboratory of Mathematics and Applications, University Abdelmalek Essaadi, Faculty of Sciences and Techniques, Boukhalef, 416 416-Tanger Principale, Morocco.Follow

Author Country (or Countries)

Morocco

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.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/120607

Recommended Citation

El Ansari, Youness; El Myr, Ali; Omari, Lahcen; and Lahrouz, Aadil (2018) "The Effect of Immigration on The Persistence and Ergodicity of a Stochastic SIS Model for Transmission of Disease," Applied Mathematics & Information Sciences: Vol. 12: Iss. 6, Article 7.
DOI: http://dx.doi.org/10.18576/amis/120607
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss6/7