%0 Journal Article
%T Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention
%A Waema R. Mbogo
%A Livingstone S. Luboobi
%A John W. Odhiambo
%J ISRN Biomathematics
%D 2013
%R 10.1155/2013/103708
%X 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 shows 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 the education of the infected patients. Comparing simulated data before and after treatment indicates the importance of combined therapeutic intervention and intracellular delay in having low, undetectable viral load in HIV-infected person. 1. Introduction Since HIV pandemic first became visible, enormous mathematical models have been developed to describe the immunological response to infection with human immunodeficiency virus (HIV). Mathematical modeling has proven to be valuable in understanding the dynamics of infectious diseases with respect to host-pathogen interactions. When HIV enters the body, it targets all the cells with CD4 receptors including the CD4 T cells. The knowledge of principal mechanisms of viral pathogenesis, namely, the binding of the retrovirus to the gp120 protein on the CD4 cell, the entry of the viral RNA into the target cell, the reverse transaction of viral RNA to viral DNA, the integration of the viral DNA with that of the host, and the action of viral protease in cleaving viral proteins into mature products, has led to the design of drugs (chemotherapeutic agents) to control the production of HIV. Chronic HIV-infection causes gradual depletion of the CD4 T-cell poll and, thus, progressively compromises the host¡¯s immune response to opportunistic infections, leading to acquired immunodeficiency syndrome (AIDS) [1]. With the spread of the HIV-AIDS pandemic and in the absence of an ¡°effective¡± vaccine or cure, therapeutic interventions are still heavily relied on. Several research studies have been carried out in the recent past, both theoretically and experimentally, to analyse the impact of therapy on the viral load in HIV-infected persons in order to ascertain the effectiveness of the treatment (see,
%U http://www.hindawi.com/journals/isrn.biomathematics/2013/103708/