Masters Degrees (Mathematical Sciences)

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Browsing Masters Degrees (Mathematical Sciences) by Subject "AIDS (Disease)"

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    Modelling the effect of HIV on age-specific incidence of active TB disease : a comparison between Taiwan and Cape Town Metropole
    (Stellenbosch : Stellenbosch University, 2012-03) Winkler, Dietrich Maximilian Albert; Nyabadza, Farai; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: See full text
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    Modelling the role of amelioration and drug lords on drug epidemics and the impact of substance abuse on the dynamics of HIV/AIDS
    (Stellenbosch : Stellenbosch University, 2011-12) Njagarah, Hatson John Boscoh; Farai, Nyabadza; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences.
    ENGLISH ABSTRACT: Substance abuse is an imminent danger on the health of both substance users and nonusers. In general, abuse of psychoactive substances is associated with high risk behaviour, mortality and morbidity. The drug use cycle involves inextricably intertwined variants such as production, trading and usage of both licit and illicit addictive substances. The dynamics of substance use involve initiation, addiction, rehabilitation/treatment and quitting/ recovery. In response to supply and abuse of monster drugs, control strategies such as law enforcement and rehabilitation have been stepped up to reduce access to drugs by targeting drug kingpins and harm reduction respectively. In this thesis, we model the factors affecting the prevalence of substance abuse, the effect of drug lords on the prevalence of substance abuse, and the impact of substance abuse on the prevalence of HIV/AIDS. We formulate mathematical models based on systems of autonomous differential equations describing the dynamics of the sub- populations involved in the drug using cycle. We examine the effects of amelioration, rehabilitation/treatment and re- initiation on the prevalence of substance abuse. Our results suggest that, recruitment into rehabilitation and amelioration in the presence of quitting for light users reduce the prevalence of substance abuse; re-initiation and amelioration without quitting for light users increase the prevalence of substance abuse. Our assessment of the impact of drug lords and the effect of law enforcement on drug epidemics shows that, the presence of drug lords seriously constraints the efforts to reduce substance abuse since they increase access to drugs. However, law enforcement if stepped up in response to the population of drug lords, greatly reduces the prevalence of substance abuse. Given the associated influence of drugs on high risky behaviour, as a cofactor for sexually transmitted infections, we assess the influence of substance abuse on the prevalence of Human Immunodeficiency Virus (HIV). Our results show that dissemination of information regarding HIV and drug use reduces HIV prevalence whereas, there is faster spread of the epidemic and high prevalence with increased sexual contact.