Dynamical properties and thresholds of an HIV model with super-infection.

Super-infection by multiple HIV-1 subtypes, previously thought restricted to high risk groups, has now been reported in the general heterosexual populations at relatively the same incidence rate as in high risk groups. We present a simple deterministic HIV model with super-infection by two HIV-1 subtypes. Mathematical characteristics including the basic reproductive number $(\mathcal{R}_0)$, invasion threshold $(\mathcal{R}_{21},\mathcal{R}_{12})$ and conditions for asymptotic stability are derived. In the absence of super-infection the model exhibits competitive exclusion, and all equilibria are globally attracting if they exist except for the disease free which is a saddle for $\mathcal{R}_0>1.$ The results show that the subtype with the dominant reproductive number exceeding unity dominates the weaker subtype forcing it to extinction regardless of the size of the reproductive number. On the other end, super-infection may promote subtype co-existence whenever the minimum of the subtype specific reproductive numbers $(\mathcal{R}_1,\mathcal{R}_2)$ and the invasion reproductive numbers $(\mathcal{R}_{12},\mathcal{R}_{21})$ exceed unity. Our results demonstrate that if the partial reproductive numbers $(\mathcal{R}_1~\mbox{and}~\mathcal{R}_2 )$ and the invasion reproductive number for the weaker subtype $(\mathcal{R}_{21})$ satisfy $\mathcal{R}_2<1,~\mathcal{R}_1>1~\mbox{and}~\mathcal{R}_{21}>1,$ then primary infection by subtype $1$ may stay the extinction of subtype $2$ despite its relatively low reproductive fitness. For certain parameter ranges, hysteresis (including backward bifurcation) occurs with possible differences in the asymptotic level of disease prevalence. Super-infection may thus facilitate the continued re-generation of reproductively noncompetent subtypes whose subtype specific reproductive numbers will be less than unity while at the same time allowing for the mutual coexistence and persistence of multiple strains. Persistence and co-existence of multiple strains has detrimental effect on vaccine design and development and administration of ART where one or more of the strains are drug resistant.

Mathematical modeling of the HIV/Kaposi's sarcoma coinfection dynamics in areas of high HIV prevalence.

We formulate a deterministic system of ordinary differential equations to quantify HAART treatment levels for patients co-infected with HIV and Kaposi's Sarcoma in a high HIV prevalence setting. A qualitative stability analysis of the equilibrium states is carried out and we find that the disease-free equilibrium is globally attracting whenever the reproductive number ℛk < 1. A unique endemic equilibrium exists and is locally stable whenever ℛk > 1. Therefore, reducing ℛk to below unity should be the goal for disease eradication. Provision of HAART is shown to provide dual benefit of reducing HIV spread and the risk of acquiring another fatal disease for HIV/AIDS patients. By providing treatment to 10% of the HIV population, about 87% of the AIDS population acquire protection against coinfection with HIV and Kaposi's Sarcoma (KS). Most sub-Sahara African countries already have programmes in place to screen HIV. Our recommendation is that these programmes should be expanded to include testing for HHV-8 and KS counseling.

Investigating alcohol consumption as a risk factor for HIV transmission in heterosexual settings in sub-Saharan African communities.

Alcohol consumption and abuse is widespread in sub-Saharan Africa where most HIV infections occur and has been associated with risky sexual behaviors. It may therefore be one of the most common, potentially modifiable HIV risk factors in this region. A deterministic system of ordinary differential equations incorporating heterogeneity and biased sexual preferences is formulated to assess the effects of alcohol consumption on the transmission dynamics of the disease in heterosexual settings. Extensive qualitative analysis of the model is carried out and epidemic threshold such as the alcohol-induced reproductive number (RA), and equilibria are derived and their stabilities examined. The disease-free equilibrium is found to be globally attracting whenever the reproductive number is less than unity. In the model, heterosexuality is the source of transmissions, and therefore, targeting a reduction of the basic reproductive number (R0) should be primary objective for any intervention programme. We show that the preference to form partnerships amongst the heterogeneous groups influences the severity of disease and its evolution, and consequently the rate of partnership formation between females and alcohol consumers and their relative infectiousness over nondrinkers has a huge positive correlation with the alcohol-induced reproductive number and hence the epidemic. The proportion or absolute number of drinkers is shown to have minimal influence on the disease dynamics, and in a community with alcohol consumers, it is more prudent to reduce their risk sexual behavior rather than to fight the spread of alcohol consumption. Thus, intervention measures targeted at reducing heterogeneous group interactions and behavior change are the key to disease control in these settings.