# DISCRETIZATIONS OF A FRACTIONAL ORDER LOGISTIC EQUATION ARISING FROM A SIMPLE SI-TERRORIST MODEL

#### Authors:

Asep K. Supriatna,Asep Sholahuddin,Hennie Husniah,

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.02.00006

#### Keywords:

SI-terrorist model,logistic differential equation,fractional order,piecewise constant argument,

#### Abstract

The simplest model of terrorist growth model consists of two subpopulations, namely the susceptible subpopulation (S) and the militant or infected and infectious subpopulation (I). The model is governed by a coupled of differential equation reflecting the growth of the susceptible and infected subpopulations. Assuming a constant human population, the system can be reduced to a logistic differential equation. In this paper  a fractional order delayed logistic equation is discussed and  the discretization  in the form of piecewise constant argument is used to find the solution. We use the first and the second order discretization method in the numerical scheme and investigate the effect of the fractional order in the growth of the underlying population modelled by the equation. We found that in general the discretization method can mimic the behavior of the original logistic equation for some parameters. However, destabilizing effect may occur depending on the combination of the values of related parameters, such as the fractional order, the intrinsic growth rate, and the piecewise constant argument parameter.

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