Some state space models of HIV pathogenesis under treatment by anti-viral drugs in HIV-infected individuals

In this paper we have extended the model of HIV pathogenesis under treatment by anti-viral drugs given by Perelson et al. [A.S. Perelson et al., Science 271 (1999) 1582] to a stochastic model. By using this stochastic model as the stochastic system model, we have developed a state space model for the HIV pathogenesis under treatment by anti-viral drugs. In this state space model, the observation model is a statistical model based on the observed numbers of RNA virus copies over different times. For this model we have developed procedures for estimating and predicting the numbers of infectious free HIV and non-infectious free HIV as well as the numbers of different types of T cells through extended Kalman filter method. As an illustration, we have applied the method of this paper to the data of patient Nos. 104, 105 and 107 given by Perelson et al. [A.S. Perelson et al., Science 271 (1999) 1582] under treatment by Ritonavir. For these individuals, it is shown that within two weeks since treatment, most of the free HIV are non-infectious, indicating the usefulness of the treatment. Furthermore, the Kalman filter method revealed a much stronger effect of the treatment within the first 10 to 20 h than that predicted by the deterministic model.