Abstract
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 effective 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.
Highlights
T4 cells, which originate in the bone marrow and mature in the thymus gland, play a dominant role in the immune system of the human body
When the T4 cell count in such an individual drops, these cells are unable to mount an effective immune response and the individual becomes susceptible to opportunistic infections and lymphomas
The T4 cell count may be considered a marker of disease progression in an infected individual and the loss of T4 cells accounts for a major part of the immunosuppressive effect of HIV
Summary
T4 cells, which originate in the bone marrow and mature in the thymus gland, play a dominant role in the immune system of the human body. Longini et al [5] modelled the decline of T4 cells in HIV infected individuals by means of a continuous-time Markov process in which the state space consists of seven states These states are the end points of six progression T4 cell count intervals and the beginning of the first interval corresponds to the time of HIV infection and the end of the last interval synchronizes with the time of AIDS diagnosis. In the work of Wick [13], the T4 cell loss in an HIV infected individual has been analysed by proposing a model in which the rates of proliferation and programmed cell death (apoptosis) control the rise and fall of the T4 cell count In all these works, the stochastic mechanism of HIV production has not been given its due importance in understanding the decline of the T4 cell count and the status of HIV progression in infected individuals.
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