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Dynamically consistent discrete epidemic model with modified saturated incidence rate. (English) Zbl 1293.37035

Summary: A nonstandard finite difference scheme is constructed to solve a SIR epidemic model with modified saturated incidence rate. The dynamical properties of the resulting discrete system are then analyzed. It is shown that the discrete system is dynamically consistent with the continuous model because it preserves essential properties of the considered model, such as positivity and boundedness of solutions, equilibrium points and their stability properties. These properties are confirmed by numerical simulations.

MSC:

37N25 Dynamical systems in biology
37M99 Approximation methods and numerical treatment of dynamical systems
92D30 Epidemiology
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References:

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