Mathematical modelling and analysis of alcohol-methamphetamine co-abuse in the Western Cape Province of South Africa

Abstract Substance/drug abuse poses a significant threat to the health and socio-economic fabric of individuals and nations. The combined abuse of alcohol and the highly addictive methamphetamine has worsened the drug epidemic in South Africa, especially in the Western Cape province. In this paper, a mathematical model is formulated to model the dynamics of alcohol and methamphetamine co-abuse. We prove that the equilibria of the submodels are locally and globally asymptotically stable when the sub-model threshold parameters are less than unity. The basic reproduction number due to co-abuse is shown to be the maximum of the two sub-model reproduction numbers. Sensitivity analysis reveals that the most sensitive parameters in the co-abuse epidemic are the alcohol and methamphetamine recruitment rates β1 and β2 respectively. The prevalence curve is indicative of a persistent drug problem in the region. Hence, the need to promote social programs that raise awareness of the dangers posed by multiple substance abuse, through educational campaigns in learning institutions, social media and health institutions. Transmission control must focus on enhancing the quitting process while promoting support services to drug users during and after treatment to minimize cases of relapse.