Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808811120210421Global dynamics of a mathematical model for propagation of infection diseases with saturated incidence rateGlobal dynamics of a mathematical model for propagation of infection diseases with saturated incidence rate69811674610.22055/jamm.2020.33801.1822FAMahmoodParsamaneshDepartment of Mathematics, Faculty of Mohajer, Isfahan Branch, Technical and Vocational University, Isfahan, Iran0000-0002-6771-7167MajidErfanianDepartment of Mathematics, Faculty of Science, University of Zabol,, Zabol, Iran0000-0001-8449-9272Journal Article20200531An epidemic model is described and introduced in which a vaccination program has been included. The model considers disease-caused death in addition to natural death, and the total population size is variable. The equilibria of the model, the disease-free equilibrium and the endemic equilibrium, are obtained and the global dynamics of the model are stated via the basic reproduction number using proper Lyapunov functions. The disease-free equilibrium is asymptotically globally stable when this quantity is less than or equal to unity and when it is greater than unity, the endemic equilibrium is asymptotically globally stable.An epidemic model is described and introduced in which a vaccination program has been included. The model considers disease-caused death in addition to natural death, and the total population size is variable. The equilibria of the model, the disease-free equilibrium and the endemic equilibrium, are obtained and the global dynamics of the model are stated via the basic reproduction number using proper Lyapunov functions. The disease-free equilibrium is asymptotically globally stable when this quantity is less than or equal to unity and when it is greater than unity, the endemic equilibrium is asymptotically globally stable.https://jamm.scu.ac.ir/article_16746_102407dfff146ada8e9eec6018079706.pdf