# Global dynamics of a mathematical model for propagation of infection diseases with saturated incidence rate

Document Type : Original Paper

Authors

1 Department of Mathematics, Faculty of Mohajer, Isfahan Branch, Technical and Vocational University, Isfahan, Iran

2 Department of Mathematics, Faculty of Science, University of Zabol,, Zabol, Iran

Abstract

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.

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Main Subjects

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### History

• Receive Date: 31 May 2020
• Revise Date: 20 November 2020
• Accept Date: 28 November 2020