EXAMINING HIV PROGRESSION MECHANISMS VIA MATHEMATICAL APPROACHES

Abstract

The progression of HIV infection to AIDS is unclear and under-examined. Many mechanisms have been proposed, including a decline in immune response, increase in replication rate, involution of the thymus, syncytium inducing capacity, activation of the latently infected cell pool, chronic activation of the immune system, and the ability of the virus to infect other immune cells. The significance of each mechanism in combination has not been studied. We develop a simple HIV viral dynamics model incorporating proposed mechanisms as parameters that are allowed to vary. In the entire parameter space, we derive two formulae for the basic reproduction number (R0) by considering the infection starting with a single infected CD4 T cell and a single virion, respectively. We then show that both formulae are equivalent. Analytically, we derive conditions for the occurrence of backward and forward bifurcations. Numerically, we perform uncertainty and sensitivity analysis to identify model parameters that significantly affect disease progression, which include the infection rate, infected cell death and proliferation rates, and viral production and clearance rates. Focusing on these identified significant parameters, a series of numerical bifurcation analyses demonstrate various HIV/AIDS progression dynamics through one or two slowly changing parameters.