A Mathematical Model for the Transmission of HIV/AIDS with Early Treatment
T. O. Akinwumi
Department of Mathematics and Computer Science, P.M.B. 002, Elizade University, Ilara-Mokin.Nigeria.
I. A. Olopade *
Department of Mathematics and Computer Science, P.M.B. 002, Elizade University, Ilara-Mokin.Nigeria.
A. O. Adesanya
Department of Mathematics and Computer Science, P.M.B. 002, Elizade University, Ilara-Mokin.Nigeria.
M. O. Alabi
Department of Physical Sciences, Chrisland University, Abeokuta, Ogun State. Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a mathematical model for the transmission of HIV/AIDS with early treatment is developed and analyzed to gain insight into early treatment of HIV/AIDS and other epidemiological features that cause the progression from HIV to full blown AIDS. We established the basic reproduction number which is the average number of new secondary infection generated by a single infected individual during infectious period. The analysis shows that the disease free equilibrium is locally and globally asymptotically stable whenever the threshold quantity is less than unity i.e. Numerical analysis shows that the early treatment of latently infected individuals reduces the dynamical progression to full blown AIDS. The result also showed that immunity boosted substances increase the red blood cells, sensitivity analysis of basic reproduction number with respect to parameters showed that effective contact rate must not exceed 0.3 to avoid endemic stage.
Keywords: HIV/AIDS, treatment; reproduction number, equilibrium points and stability