Explicit and implicit schemes for fractional–order Hantavirus model

Abstract

In this paper, the fractional–order form of a mouse population model is introduced. Some explicit and implicit schemes, which are Theta methods and nonstandard finite difference (NSFD) schemes, are implemented to give a numerical solution of nonlinear ordinary differential equation system named Hantavirus epidemic model. These methods are compared and discussed that the method preserves the positivity properties of the integer order system. The numerical solutions are illustrated by means of some graphs. Numerical results of explicit and implicit methods denote that these methods are easy and accurate when applied to fractional–order Hantavirus model.

Keywords

• explicit and implicit methods
• theta method
• nonstandard finite difference scheme
• fractional–order nonlinear differential equation systems
• mouse population model