Numerical solution of the SIR epidemic model using the non-standard finite difference method

Subject Areas : Statistics

Abdulrahman Yaghoubi ¹ , Hashem Saberi Najafi ²

1 - Department of Applied Mathematics, Saravan Branch, Islamic Azad University, Saravan, Iran.
2 - Department of Applied Mathematics, Faculty of Mathematical Sciences, Islamic Azad University, Lahijan Branch, Lahijan, Iran.

Received: 2019-09-25 Accepted : 2021-09-18 Published : 2021-11-22

Keywords: پایداری, بیماری‌های اپیدمیک, روش تفاضل متناهی غیر استاندارد, نقاط تعادل,

Abstract :

In this paper, a special case of the finite difference method which is called non-standard finite difference method is studied for the numerical solution of a mathematical model of epidemic diseases. The constructed non-standard finite difference schemes have the main properties of the continuous model such as positivity, boundedness, and stability. The stability of the equilibrium points of the system is investigated. The proposed non-standard finite difference schemes are convergent to the equilibrium points of the system. In solving nonlinear problems, one of the important advantages of this method is that nonlinear term discretized with nonlocal approximations. In most cases, non-standard finite difference schemes are stable even when large step sizes are considered. Therefore, using non-standard method will be cost-effective in dynamical systems that are studied over a large time interval. Numerical examples confirm the accuracy and efficiency of the non-standard finite difference method.Keywords: Non-Standard Finite Difference Method, SIR Model, Equilibrium Points.

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