Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates

By Yoichi Enatsu, Y. Nakata, Y. Muroya, G. Izzo, A. Vecchio. 2012

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In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number , when the infection incidence rate has a suitable monotone property.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/88caab7d8e501fdaf3e28110b355b92a65eaf1f5