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ISRN Biomathematics
Volume 2013 (2013), Article ID 103708, 11 pages
http://dx.doi.org/10.1155/2013/103708
Research Article

Stochastic Model for In-Host HIV Dynamics with Therapeutic Intervention

1Center for Applied Research in Mathematical Sciences, Strathmore University, P.O. Box 59857 00200, Nairobi, Kenya
2Department of Mathematics, Makerere University, P.O. Box 7062, Kampala, Uganda

Received 22 February 2013; Accepted 27 March 2013

Academic Editors: X.-Y. Lou and J. Suehnel

Copyright © 2013 Waema R. Mbogo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 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.