Discontinuity, Nonlinearity, and Complexity
Asymptotic Behavior of an SIS Epidemic Model with Delay
Discontinuity, Nonlinearity, and Complexity 11(1) (2022) 149160  DOI:10.5890/DNC.2022.03.013
Jaafar El Karkri
Laboratory LERMA, Mohammadia School of Engineering, Mohammed V University in Rabat, Avenue Ibn Sina, B.P 765, Agdal Rabat 10090, Morocco
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Abstract
This work deals with the qualitative behavior of a delay differential equation arising from an SIS epidemiological model. The population is assumed to be of exponential demographic structure and delay corresponds to the infectious period. A death rate caused by infection is considered. The study is based on the exponential ordering properties in the context of monotone systems. A new sufficient condition of the asymptotic stability of the endemic disease equilibrium is derived. Then we provide a new sufficient condition of global asymptotic stability of the disease free equilibrium. Moreover, the author proves that the established condition of global stability is different from that obtained in 1995 by H.W. Hethecote and P. van den Driessche. The obtained results are then illustrated by numerical simulations.
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