Modelling the dynamics of alcohol and methamphetamine co-abuse in the Western Cape Province of South Africa

[摘要] ENGLISH ABSTRACT: Clinical results have indicated that abuse of multiple drugs/substances has devastatinghealth and social consequences. The combined abuse of alcohol and the highlyaddictive methamphetamine has worsened the drug epidemic in South Africa, especiallyin the Western Cape Province. Using non-linear ordinary differential equations,we formulate a deterministic mathematical model for alcohol-methamphetamine coabuseepidemic. We prove that the growth of the co-abuse epidemic is dependenton the threshold parameters of the individual substances of abuse. The substancewith the maximum reproduction number dominates the epidemic. We also provethat the equilibria points of the co-abuse sub-models are locally and globally asymptoticallystable when the sub-model threshold parameters are less than unity. Usingparameters values derived from the sub-model fittings to data, a population estimateof co-users of alcohol and methamphetamine under treatment is estimated with aprevalence of about 1%. Although the results show of a small proportion of co-usersof alcohol and methamphetamine in the province, the prevalence curve is indicativeof a persistent problem. Numerical simulation results reveal that co-abuse epidemicwould persists when both reproduction numbers are greater than one. Results fromsensitivity analysis shows that the individual substance transmission rates betweenusers of methamphetamine and/or alcohol and the general susceptible populationare the most vital parameters in the co-abuse epidemic. This suggests the need to emphasiseon preventive measures through educational campaigns and social programsthat ensure minimal recruitment into alcohol or methamphetamine abuse. Modelanalysis using the time-dependent controls (policies) emphasizes the need to allocateeven more resources on educational campaigns against substance abuse and on effectivetreatment services that minimizes or eliminates rampant cases of relapse intosubstance abuse.

[发布机构] Stellenbosch University