Zeitschrift für AIDS und klinische Forschung

Global dynamics of a fractional order SIR epidemic model for HIV transmission with memory

Abstract

Parvaiz Ahmad Naik

In this paper, we investigate and analyze a nonlinear fractional order SIR epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate. The existence and stability of the equilibrium points are investigated. The sufficient conditions for the persistence of the disease are provided. First, we obtained a threshold value , which determines the stability of equilibria, then model equilibria are determined, and their stability analysis are considered by using fractional Routh-Hurwitz stability criterion and fractional LaSalle invariant principle. The fractional derivative is taken in Caputo sense and the numerical solution of the model is obtained by L1 scheme method which involves the memory trace that can capture and integrate all past activity. Meanwhile, by using Lyapunov functional approach, the global dynamics of the endemic equilibrium point is discussed