A non-standard numerical scheme for an alcohol-abuse model with induced-complications

The prevalence of alcohol-related fatalities worldwide is on the ascendancy not only Ghana, but worldwide. Although the ramifications of alcohol consumption have been the subject of several studies, alcoholism remains a serious concern in public health. This study investigates the dynamics of alcoholism in a population with consumption-induced complications using a deterministic Modelling framework. Using a novel technique, we determined a threshold parameter $$ which we call the basic alcohol-abuse initiation number which is similar to the basic reproduction number for infectious diseases. The model has two mutually-exclusive fixed points whose existence depend on whether or not the $$ is less or greater than unity. Global asymptotic stability of the alcohol-abuse-free fixed point is shown to be associated with $$. Further, forward bifurcation is observed to occur at $$, indicating the possibility of eradication of the phenomenon of alcoholism if $$ can be kept below unity over a sufficiently long period of time. Sensitivity analysis also revealed that the probability of initiation into alcohol-abuse by moderate drinkers ($$), followed by the probability of initiation into alcohol-abuse by heavy drinkers ($$) are the most the parameters with the most influence on $$ and consequently on alcohol-abuse persistence. A non-standard finite difference scheme is also developed to numerically simulate the model so as to demonstrate the findings derived from the analysis and also to observe the impact of some epidemiological factors on the dynamics of alcohol-abuse.