Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention

Abstract

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 propose and show the usefulness of a stochastic approach towards modeling HIV and CD4 cells Dynamics in Vivo by obtaining probability generating function, the moment structures of the healthy CD4 cell and the virus particles at any time t and the probability of HIV clearance. The unique feature is that both therapy and the intracellular delay are incorporated into the model. Our analysis show that, when it is assumed that the drug is not completely effective, as is the case of HIV in Vivo, the probability of HIV clearance depends on two factors: the combination of drug efficacy and length of the intracellular delay and also education to the infected patients. Comparing simulated data for before and after treatment indicates the importance of combined therapeutic intervention and intra-cellular delay in having low, undetectable viral load in HIV infected person.

Keywords: Intracellular delay, Therapeutic intervention, CD4 cells,Drug efficacy, stochastic model