Analysis of an epidemic model with peer-pressure and information-dependent transmission with high-order distributed delay

Abstract

In this paper, we propose and analyze a behavioral model for the spread of high-risk alcohol consumption. The model is given by ordinary differential equations and includes a convex ‘force of persuasion’ that mimics the peer-pressure. We also assume that the transmission rate depends on the current and the past history of alcohol abuse prevalence in the community and that the weight given to the past history is described by an n-order Erlangian kernel. We perform a qualitative analysis based on stability and bifurcation theory. We show that multiple endemic equilibria may coexist and that backward bifurcation takes place when the peer-pressure is strong enough. We also use a Lyapunov stability approach to find sufficient conditions ensuring that the alcohol-free equilibrium is globally stable.