Stochastic modeling of HIV dynamics within an individual and its management

Abstract

Mathematical models can facilitate the understanding of complex biomedical systems such as in HIV/AIDS. Untangling the dynamics between HIV and CD4+ cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. With that in mind, we will develop state transition systems dynamics and stochastic model that can be used to examine various alternatives for the control and treatment of HIV/AIDS, and also determine the cost of treating an HIV patient such that the expected lifetime or quality-adjusted lifetime of the patient is maximized. The AIDS epidemic is extremely dynamic; this dynamism orthogonally complicates interventions embraced for the management of the epidemic. This research is mostly motivated by the fact that eradication of the HIV virus is not attainable with the current available drugs and now the focus is not virus eradication but the management and control of the virus progression. We will develop and analyze Non-Homogeneous Semi-Markov Stochastic (NHSMS) Models of HIV biological process and compute internal transition probabilities. Specifically the models will target: the HIV internal dynamics in an infected person, defined by CD4+ levels and Viral load, and the disease control and management strategies put in place. Secondly we will use Non-Homogeneous Semi-Markov Reward (NHSMR) processes to determine the cost of treating an HIV patient, and lastly, we consider the revenue generated by such person (as well as the expert advice by such infected person into various projects) such that the Cost Benefit Analysis (CBA) can also be conducted.