Abstract
A compartmentalized deterministic mathematical model for the dynamics of HIV/AIDS under the use of male and female condoms has been formulated and studied qualitatively. Disease-free equilibria of the sub-models have been found to be locally and asymptotically stable. Stability results revealed threshold values for the proportions of susceptible and infected subpopulations that must use condom in order to achieve control, and possibly, eradication of HIV/AIDS in heterosexual populations. Condom use rate for the susceptible subpopulations has been found to be bounded above by the population’s birth rate, while that of the infected subpopulations is bounded below by a given threshold.KEYWORDS: Locally and asymptotically stable, disease-free equilibrium, HIVAIDS control
Highlights
Research has revealed a great deal of valuable medical, scientific and public health information about the human immunodeficiency virus (HIV), the causative agent for acquired immunodeficiency syndrome (AIDS), (Avert, 2008)
The HIV prevalence is much lower in Nigeria than in other African countries such as South Africa and Zambia, the size of Nigeria’s population meant that by the end of 2007, there were an estimated 2,600,000 people infected with HIV, which is rather on the high side (UNAIDS, 2008)
Our main objective in this paper is to investigate the existence of the conditions for eradication of HIV in heterosexual populations under the use of male and female condoms
Summary
Research has revealed a great deal of valuable medical, scientific and public health information about the human immunodeficiency virus (HIV), the causative agent for acquired immunodeficiency syndrome (AIDS), (Avert, 2008). Our main objective in this paper is to investigate the existence of the conditions for eradication of HIV in heterosexual populations under the use of male and female condoms. Transforming the model equations into proportions has the advantage of reducing the total number of equations in the model, giving the equations in epidemiologically meaningful forms (for instance, the proportion of infected persons defines the prevalence of infection), (Avert, 2008). Using these substitutions in equations (2.1) – (2.8) and considering (2.9) to (2.12), we obtain the model equations in ( ) proportions as given by equations (3.1) – (3.6). We apply Hurwitz criterion (see David (1997) and Weisstein (2008)) to study the stability of the disease-free equilibrium (DFE) states of the various sub-models in this paper
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