Modeling Uncertainty pp 95-115 | Cite as

# Stochastic Modelling of Early HIV Immune Responses Under Treatment by Protease Inhibitors

## Abstract

It is well documented that, in any ases, most f the free HIV are generated in the lymphoid tissues rather than in the plasma. This is especially true in the late stage of HIV pathogenesis because in this stage, the total number of **CD4**^{(+)} T cells in the plasma is very small, whereas the number of free HIV in the plasma is very large. In this paper we have developed a state space model in plasma involving net flow of HIV from lymph nodes, extending the original model of Tan and Xiang (1999). We have applied this model and the theory to the data of a patient (patient No.104) considered in Perelson et al. (1996), n which RNA virus copies per **mm**^{3} were observed on 18 occasions over a three week period. This patient was treated by a protease inhibitor, ritonavir, so that a large number of non-infectious HIV was generated by the treatment. For this patient, by using the state space model over the three week span, we have estimated the numbers of productively HIV-infected T cells, the total number o f infectious HIV, as well as the number of non-infectious HIV. Our results showed that within this period, most of the HIV in the plasma was non-infectious, indicating that the drug is quite effective.

## Keywords

Infectious HIV lymph nodes Monte Carlo studies non-infectious HIV protease inhibitors state space models stochastic differential equations## Preview

Unable to display preview. Download preview PDF.

## Publications of Sid Yakowitz

- Cavert, W., D.W. Notermans, K. Staskus, et al. (1996).
*Kinetics of response in lymphoid tissues to antiretroviral therapy of HIV-1 infection*. Science,**276**, p. 960–964.Google Scholar - Cohen, O.J., G. Pantaleo, G.K. Lam, and A.S. Fauci. (1997).
*Studies on lymphoid tissue from HIV-infected individuals: Implications for the design of therapeutic strategies*. In: “Immunopathogenesis of HIV Infection, A.S. Fauci and G. Pantaleo (eds.)”. Springer-Verlag, Berlin, p. 53–70.CrossRefGoogle Scholar - Cohen, O.J., D. Weissman, and A.S. Fauci. (1998).
*The immunopathpgenesis of HIV infection. In: “Fundamental Immunology, Fourth edition.” ed. W.E. Paul, Lippincott-Raven Publishers, Philadelphia, Chapter 44, p. 1511–1534*.Google Scholar - Haase, A.T., K. Henry, M. Zupancic, et al. (1996).
*Quantitative image analysis ofHIV-1 infection in lymphoid tissues*. Science,**274**, p. 985–989.Google Scholar - Fauci, A.S. and G. Pantaleo. (Eds.) (1997).
*Immunopathogenesis of HIV Infection*. (Springer-Verlag, Berlin, 1997.)Google Scholar - Fauci, A.S. (1996).
*Immunopathogenic mechanisms of HIV infection. Annals of Internal Medicine***124**, p. 654–663.CrossRefGoogle Scholar - Kirschner, D.E. and G.F. Webb. (1997).
*Resistance, remission, and qualitative differences in HIV chemotherapy*. Emerging Infectious Diseases,**3**, p. 273–283.CrossRefGoogle Scholar - Lafeuillade, A., C. Poggi, N. Profizi, et al. (1996).
*Human immunodeficiency virus type 1 kinetics in lymph nodes compared with plasma*. The Jour. Infectious Diseases,**174**, p. 404–407.CrossRefGoogle Scholar - Mitter, J.E., B. Sulzer, A.U. Neumann, and A.S. Perelson. (1998).
*Influence of delayed viral production on viral dynamics in HIV-1 infected patients*. Math. Biosciences,**152**, p.. 143–163.CrossRefGoogle Scholar - Perelson, A.S., A.U. Neumann, M. Markowitz, et al. (1996).
*HIV-1 dynamics in vivo: Virion clearance rate, infected cell life-span, and viral generation time*. Science,**271**, p. 1582–1586.Google Scholar - Perelson, A.S., O. Essunger, Y.Z. Cao, et al. (1997).
*Decay characteristics of HIV infected compartments during combination therapy*. Nature,**387**, p. 188–192.CrossRefGoogle Scholar - Piatak, M. Jr., M.S. Saag, L.C. Yang, et al. (1993). t
*High levels of HIV-1 inplasma during all stages of infection determined by competitive PCR*. Science,**259**, p. 1749–1754.Google Scholar - Tan, W.Y. and H. Wu. (1998).
*Stochastic modeling of the dynamics of CD4*^{(+)}*T cells by HIV infection and some Monte Carlo studies*. Math. Biosciences,**147**, p. 173–205.MathSciNetCrossRefGoogle Scholar - Tan, W.Y. and Z.H. Xiang. (1998).
*State Space Models for the HIV pathogenesis. In: “Mathematical Models in Medicine and Health Sciences”, eds. M.A. Horn, G. Simonett and G. Webb*. (Vanderbilt University Press, Nashville, TN, 1998), p. 351–368.Google Scholar - Tan, W.Y. and Z.H. Xiang. (1999).
*A state space model of HIV pathogenesis under treatment by anti-viral drugs in HIV-infected individuals*. Math. Biosciences,**156**, p. 69–94.MathSciNetCrossRefGoogle Scholar - Tan, W.Y. and Z.Z. Ye. (1999).
*Stochastic modeling of HIV pathogenesis under HAART and development of drug resistance*. (Proceeding of the International 99’ ISAS meeting, Orlando, Fl. 1999.)Google Scholar - Tan, W.Y. and Z.Z. Ye. (2000).
*Assessing effects of different types of HIV and macrophage on the HIV pathogenesis by stochastic models of HIV pathogenesis in HIV-infected individuals*. Jour. Theoretical Medicine,**2**, p. 245–265.CrossRefGoogle Scholar - Weiss, R.A. (1996).
*HIV receptors and the pathogenesis of AIDS*. Science,**272**, p. 1885–1886.Google Scholar