Analysis of the SAITS alcoholism model on scale-free networks with demographic and nonlinear infectivity

Abstract

A more realistic alcoholism model on scale-free networks with demographic and nonlinear infectivity is introduced in this paper. The basic reproduction number $R_{0} $ is derived from the next-generation method. Global stability of the alcohol-free equilibrium is obtained. The persistence of our model is also derived. Furthermore, the SAITS model with nonlinear infectivity is also investigated. Stability of all the equilibria and persistence are also obtained. Some numerical simulations are also presented to verify and extend our theoretical results.

Keywords

• alcoholism
• scale-free networks
• demographic
• stability
• nonlinear infectivity