Stability analysis of a fractional-order SIS model on complex networks with linear treatment function

Abstract

Abstract In recent years, many research works have been focusing on the propagation dynamics of infectious diseases in complex networks, and some interesting results have been obtained. The main purpose of this paper is to investigate the stability of a fractional SIS model on complex networks with linear treatment function. Based on the basic reproduction number, the stability of the disease-free equilibrium point and the endemic equilibrium point is analyzed in detail. That is, when R0≤1 $R_{0}\le1$, the disease-free equilibrium point is globally asymptotically stable and the disease will die out ultimately; when R0>1 $R_{0}>1$, there exists a unique endemic equilibrium point, and both the disease-free equilibrium point and the endemic equilibrium point are stable and the disease will not spread to all individuals. Finally, numerical simulations are presented to demonstrate the theoretical results. Moreover, the influence of the fractional-order parameter and the coefficient of the linear treatment function on the decay rate of the infectious is depicted separately.

Keywords

• Fractional-order
• Stability
• Treatment function
• Complex network