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