Global dynamics for a SIRI discrete delay epidemic model

Mohamed El Fatini, Aziz Laaribi, Stanislas Ouaro, Regragui Taki


In this work, we study a SIRI epidemic model with incidence rate and latent period. A SIRI epidemiological model in a population consists of a system with three compartments : susceptibles, infectives, and removed, labeled by S ; I ; R: In this model, susceptibles become infectious, then are removed with temporary immunity, and then become infectious again. The SIRI model is appropriate for some disease such as human and bovine tuberculosis, and herpes, in which recovered individuals may revert back to the infective class due to reactivation of the latent infection or incomplete treatment. We study this type of epidemic model to understand the principle of disease transmissions with incidence rate. Especially we derive conditions for the global asymptotic stability of the disease-free and endemic equilibria of the model by using Lyapunov’s functionals.


Epidemiological model, Disease relapse, Latent period, Time delay, Stability

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