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A Dynamically Consistent Nonstandard Numerical Scheme for Epidemic Model with Saturated Incidence Rate

A. Suryanto

Abstract


A competitive numerical scheme for SIR epidemic model with saturated incidence rate is developed by applying nonstandard finite difference (NSFD) scheme. The local dynamics of the numerical scheme is analyzed and compared with the continuous model. We prove analytically that, for any size of time step, the NSFD scheme preserves some essential dynamical properties related to the considered model, such as positivity of the solutions, conservation population law, equilibrium points and their stability properties. Such dynamical properties are also confirmed by numerical simulations. It is shown numerically that explicit Euler method and several standard MATLAB procedures for solving first order ODE system may fail to maintain the dynamical properties.

Keywords


Dynamically consistent, Nonstandard finite difference scheme, SIR epidemic model, Saturated incidence rate

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