Discontinuity, Nonlinearity, and Complexity
Monotone Dynamical Systems Theory for Epidemiological Models with Delay: A New Approach with Applications
Discontinuity, Nonlinearity, and Complexity 8(4) (2019) 369377  DOI:10.5890/DNC.2019.12.002
Jaafar El Karkri, Khadija Niri
Laboratory MACS, Department of Mathematics and Computer Science, Faculty of Sciences, University Hassan II Ain Chock, B.P.5366Maarif, Casablanca 20100 Morocco
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Abstract
Monotone dynamical systems theory is an efficient and powerful tool for the study of dynamical systems asymptotic behaviour. However it is rarely used in mathematical epidemiology. In this paper we present a comparison between two different approaches of convergence and stability for dynamical systems. We prove that the convergence in the sense of the monotone dynamical systems theory is equivalent to the uniform convergence in the classical Lyapunov theory. Then we provide a stability analysis of an SIS
epidemiological model based on the monotone approach. Numerical simulations illustrate our theoretical results.
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