Abstract:
The success of antiretroviral drugs (ARVs) to control Human Immunodeficiency Virus (HIV) and
Acquired Immune Deficiency Syndrome (AIDS) and eliminating the condition depends on the accurate
estimation of prognostic indicators of treatment outcomes. Mathematical models using differential equations
were formulated to describe the interaction of the Immune system with HIV pathogens. Proliferation rate of
naive and HIV specific activated effector cells was investigated to determine the threshold efficacy of immuno-
stimulants for perfect immune response. The conditions for the existence and stability of disease free equilibrium
(DFE) and endemic equilibrium point (EEP) were determined. It was found that DFE exists if the Reproductive
ratio, R 0 < 1 and EEP exists when R 0 > 1. Epidemiological and demographic parameters of HIV/AIDS and
immune response data analyzed showed that in the absence of immuno-stimulants, R 0 = 4, and the introduction of
immuno-stimulants increased the proliferation rate of effector cells, thus improving the immune response time to
eliminate the infection. This means R 0 reduces from R 0 = 4 to values less than one. Simulation results with
varying efficacy levels of immuno-stimulants showed that the EEP becomes extinct and DFE is stable if the drug
efficacy is at e = 75.4%. The results also showed that the normal cell homeostatic rate of N = 2 daughter cells
is activated by use of immuno-stimulants to increase to multiples of N = 3.49 memory cells during a re-
emergence of the disease.
