Qualitative Analysis of a SIR Epidemic Model with a Nonlinear Relapse and Incidence Rate Stochastically Perturbed

Authors

Abdelaziz Assadouq, Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and Techniques, B.P. 416-Tanger Principale, Tanger, Morocco.Follow
Adel Settati, 1 Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Sciences and Techniques, B.P. 416-Tanger Principale, Tanger, Morocco.Follow
Ali El Myr, Laboratory of Computer Sciences and Modeling, Department of Mathematics, Faculty of Sciences Dhar-Mehraz B.P. 1796-Atlas, Fez, Morocco.Follow

Author Country (or Countries)

Morocco.

Abstract

In this paper, we analyze a stochastic SIR epidemic model in a constant population with a relapse and nonlinear perturbation. First, we illustrate show that the system has a unique global positive solution that belongs to a positively invariant set. Then, we obtain sufficient conditions for the extinction and persistence in the mean. Finally, numerical simulations are carried out to illustrate the theoretical results.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/130613

Recommended Citation

Assadouq, Abdelaziz; Settati, Adel; and El Myr, Ali (2019) "Qualitative Analysis of a SIR Epidemic Model with a Nonlinear Relapse and Incidence Rate Stochastically Perturbed," Applied Mathematics & Information Sciences: Vol. 13: Iss. 6, Article 13.
DOI: http://dx.doi.org/10.18576/amis/130613
Available at: https://digitalcommons.aaru.edu.jo/amis/vol13/iss6/13