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

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Date
2012-12-31Author
Enatsu, Y.
Nakata, Y.
Muroya, Y.
Izzo, G.
Vecchio, A.
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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.