A Probabilistic SIRI Epidemic Model Incorporating Incidence Capping and Logistic Population Expansion

Authors

Soulaimane Aznague, Laboratory of Mathematics and Applications, FSTT, Abdelmalek Essaadi University, Tetouan, MoroccoFollow
Mourad El Idrissi, Laboratory of Mathematics and Applications, FSTT, Abdelmalek Essaadi University, Tetouan, MoroccoFollow
Abdeladim Nait Brahim, Laboratory of Mathematics and Applications, FSTT, Abdelmalek Essaadi University, Tetouan, MoroccoFollow
Bilal Harchaoui, Laboratory of Mathematics and Applications, FSTT, Abdelmalek Essaadi University, Tetouan, MoroccoFollow
Saloua Boutouil, Laboratory of Mathematics and Applications, FSTT, Abdelmalek Essaadi University, Tetouan, MoroccoFollow
Adel Settati, Laboratory of Mathematics and Applications, FSTT, Abdelmalek Essaadi University, Tetouan, MoroccoFollow

Author Country (or Countries)

Morocco

Abstract

This study presents a newly developed stochastic SIRI epidemic model, which combines logistic growth with a saturation incidence rate. This research mainly examines the presence and uniqueness of positive solutions within the formulated model. Furthermore, we aim to analyze the long-term performance of the system and provide valuable insights into disease extinction in a population. Our investigation delves into the conditions required for disease extinction, which are crucial in predicting and controlling the spread of deadly diseases. To substantiate our assertions, we have devised a stochastic Lyapunov function, which serves as a robust mathematical framework for demonstrating the presence of a discernible stationary ergodic distribution. This mathematical foundation significantly contributes to the understanding of model behavior. To complement our analytical findings, we conduct numerical simulations, which reinforce our results and provide a comprehensive understanding of the behavior of our proposed model, and open new avenues for future research in this area.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/170505

Recommended Citation

Aznague, Soulaimane; El Idrissi, Mourad; Nait Brahim, Abdeladim; Harchaoui, Bilal; Boutouil, Saloua; and Settati, Adel (2023) "A Probabilistic SIRI Epidemic Model Incorporating Incidence Capping and Logistic Population Expansion," Applied Mathematics & Information Sciences: Vol. 17: Iss. 5, Article 5.
DOI: http://dx.doi.org/10.18576/amis/170505
Available at: https://digitalcommons.aaru.edu.jo/amis/vol17/iss5/5