Mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers (Q1989035)

Summary: In this paper, we present a continuous mathematical model \(PMH T^r T^p Q\) of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number \(R_0\). We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number \(R_0\). The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium \(E^0\) when \(R_0\leq 1\). When \(R_0>1\), drinking present equilibrium \(E^*\) exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium \(E^*\).