Modelling T4 cell count as a marker of HIV progression in the absence of any defense mechanism
The T4 cell count, which is considered one of the markers of disease progression in an HIV infected individual, is modelled in this paper. The World Health Organisation has recently advocated that countries encourage HIV infected individuals to commence antiretroviral treatments once their T4 cell count drops below 350 cells per ml of blood (this threshold was formerly 200 cells per ml of blood). This recommendation is made because when the T4 cell count is low, the T4 cells are unable to mount an eective immune response against antigens and any such foreign matters in the body, and consequently the individual becomes susceptible to opportunistic infections and lymphomas. A stochastic catastrophe model is developed in this paper to obtain the mean, variance and covariance of the uninfected, infected and lysed T4 cells. The amount of toxin produced in an HIV infected person from the time of infection to a later time may also be obtained from the model. Numerical illustrations of the correlation structures between uninfected and infected T4 cells, and between the infected and lysed T4 cells are also presented.
Key words: Toxin, uninfected T4 cells, infected T4 cells, lysed T4 cells, catastrophe stochastic model.