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

  • Wai-Yuan Tan
  • Zhihua Xiang
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 46)


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 mm3 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.


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


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Publications of Sid Yakowitz

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Copyright information

© Springer Science + Business Media, Inc. 2002

Authors and Affiliations

  • Wai-Yuan Tan
    • 1
  • Zhihua Xiang
    • 2
  1. 1.Department of Mathematical SciencesThe University of MemphisMemphis
  2. 2.Organon Inc.West Orange

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