Fractional order heroin epidemic dynamics

Abstract

Using illicit drugs has been on growth in all over the world especially in the USA, Europe and Asia. It is very harmful to society; it is the fourth foremost cause of death in the United States when taking overdose drug (about the same as motor vehicle crashes). A drug that has a significant detrimental effect on a population as a whole is heroin, above all illegal substances. This work discussesthenon-classical mathematical model of White and Comiskey, demonstrating heroin epidemics. We present the existence of stable equilibrium numerically & mathematically. We will apply two methods (i) Adams Bashforth PECE method and (ii) Grunwald-Letnikovmethod (GLM) and simulate the model using Matlab software package.