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A Probabilistic SIRI Epidemic Model Incorporating Incidence Capping and Logistic Population Expansion |
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PP: 773-789 |
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Author(s) |
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Soulaimane Aznague,
Mourad El Idrissi,
Abdeladim Nait Brahim,
Bilal Harchaoui,
Saloua Boutouil,
Adel Settati,
Aadil Lahrouz,
Mhamed El Merzguioui,
Jamal El Amrani,
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Abstract |
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| 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.
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