Incorporating convex incidence rate and public awareness program in modelling drinking abuse and novel control strategies with time delay

In the recent past, a mathematical model has been formulated showing the impact of public health education campaigns and linear relapse on drinking abuse. The purpose of the present study is to provide a modified variant of this drinking abuse model. Hence, initially, our model incorporates a convex incidence rate, which will show the scenario that if an individual quits alcohol abuse and after a short interval he/she restarts alcohol use. In addition, it will examine the existence of Hopf bifurcation as well as study stability analysis and the time delay is used in the formulation of the delayed drinking model. Based on some auxiliary conditions, it is shown that the underlying model is globally asymptotically stable. Furthermore, to construct a controlled system, novel control variables have been introduced, and results related to controlling the abuse in society are carried out. Lastly, to show the authenticity of the obtained results, graphical representations are given for stability, instability and impact of the suggested control variables. In this research endeavour, we conclude that mathematical models are useful tools for knowing the dynamics of drinking abuse and for suggesting policy-makers towards more useful and feasible policies to contain this abuse.