A mathematical model of the effect of immune-stimulants on the immune response to HIV infection

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.