Stability Analysis of the Transmission Dynamics of HIV/AIDS in the Presence of Treatment and Condom Usage

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Author(s) S. Abdulrahman | M. Bawa | Y. B. Aliyu | A. I. Ajike
Pages 336-352
Volume 2
Issue 4
Date April, 2013
Keywords HIV/AIDS, Effective basic reproduction number, Stability, Bifurcation analysis
Abstract

We developed and analysed a new a mathematical model for the dynamics of Human Immunodeficiency Virus infection/Acquired Immunodeficiency Syndrome (HIV/AIDS) in a population with vital dynamics, incorporating vertical transmission, sexual maturity and the effect of public enlightenment campaign with respect to sexual behaviour change and treatment as control measures. We obtained the effective basic reproduction number, which can be used to control the transmission of the disease and hence, established the conditions for local and global stability of the disease free equilibrium. Bifurcation analysis was carried out using centre manifold theory which reveals a subcritical (backward) bifurcation for the model. Numerical simulations validated the analytical results and further reveal that treatment with Antiretroviral Drugs Therapy (ART) by even 25% of the sexually active HIV+ individuals will lead to a reduction of the disease morbidity, while ART treatment by 75% of HIV+ children and/or AIDS infected individuals as encourage by World Health Organisation (WHO) does not have any positive impact on disease morbidity. Furthermore, condom usage (as the only control measure) must be as high as 75% before any positive result is achieved.

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