Stochastic analysis of AIDS epidemiology

In this thesis, some issues about the human immunodeficiency virus (HIV) and acquired immunodeficiency syndrome (AIDS) have been addressed by concentrating on the stochastic modelling of the dynamics of the viruses. The aim of this thesis is to determine parameters such as the mean number of free HIV, infectious free HIV and non-infectious free HIV which are essential in determining incubation period of the virus, the disease progression of an infected individual and the efficacy of the treatment used. This thesis comprises of six chapters. The first two chapters are introductory to the viruses and reasons why HIV-1 is given priority over HIV-2 are given. The pathogenesis of the virus is addressed. This is because knowledge of the pathogenesis and strains of the virus has become essential in the study of HIV in vivo dynamics which is still paving ways into extensive research of the ways to contain the disease better. In chapter three the distribution functions of the HIV incubation period and seroconversion time are determined via stochastic models by building on previous work of Lui et al. (1988) and Medley et al. (1988). Also AIDS incidence projection was done using the Backcalculation method. Chapter four deals with the formulation of stochastic model of the dynamics of HIV in an infected individual. Two stochastic models are proposed and analysed for the dynamics of the viral load in a HIV infected person and the multiplication process of the virions inside an infected T4 cell. Also a numerical illustration of the stochastic models derived is given. In chapter five, the T4 cell count which is considered one of the markers of disease progression in HIV infected individual is examined. WHO has recently advocated that countries encourage HIV infected individuals to commence antiretroviral treatments once their T4 cell count is 350 cells per ml of blood. This is 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. We developed a stochastic catastrophe model to obtain the mean, variance and covariance of the uninfected, infected and lysed T4 cells; also the amount of toxin produced in a HIV infected person from the time of infection to the present time is derived. A numerical illustration of the correlation structure between uninfected and infected T4 cells, and infected and lysed T4 cells is portrayed. Antiretrioviral treatments were introduced while we await a cure. Treatment with single drug failed due to the fact that HIV evolved rapidly because of its high replication rate. Thus drug resistance to single therapeutic treatment in HIV infected individuals has promoted research into combined treatments. In chapter six a stochastic model under combined therapeutic treatment is derived. Mean numbers of free HIV, infectious free HIV and non-infectious free HIV are obtained. Variance and co-variance structures of our parameters were obtained unlike in previous work of Perelson et al. (1996), Tan and Xiang (1999).Thesis (PhD)--University of Pretoria, 2009.Statisticsunrestricte

A stochastic point process model of the incubation period of a HIV infected individual

The inability to get people to regularly test and know their HIV status has caused the widespread unavailability of correct and comprehensive data on HIV infection especially the time at which an individual was first infected. Hence, mathematical scientists have relied extensively on inference obtained from small samples to estimate the HIV incubation and seroconversion times. We set out to obtain in this paper, (i) the distribution functions of the HIV incubation period and seroconversion time by considering the stochastic behaviours of the members of the population under discussion, and (ii) the method of estimation that gives the best parameter estimate by building on previous work of Lui et al. (1988) and Medley et al. (1988). We obtained a one-parameter family distribution for the incubation period and a two-parameter family distribution for the seroconversion time. Data on homosexual individuals were used since we built on past work of Lui et al. (1988). Also AIDS incidence projection was done using the backcalculation method. However, the shortfall of the back-calculation method was not addressed in this paper as this is meant for further research.Thanks to NRF for funding this project.http://www.sastat.org.za/journal.ht

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 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 de- veloped 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

A stochastic model of the dynamics of HIV under a combination therapeutic intervention

Drug resistance to single therapeutic treatment in HIV infected individuals has promoted research into combined treatments. In this paper we propose a stochastic model under combined therapeutic treatment by extending the model of HIV pathogenesis under treatment by anti-viral drugs given in [Perelson AS, Neumann AU, Markowits M, Leonard JM & Ho DD, 1996, HIV-1 dynamics in vivo virion clearance rate, infected cell life span, and viral generation time, Science New Series, 271, pp. 1582-1586]. Variance and co-variance structures of variables are obtainable via this approach in addition to the mean numbers of free HIV, infectious free HIV and non-infectious free HIV that were obtained by Perelson et al. Comparing simulated data for before and after treatment indicates the importance of combined treatment and its overall e ect(s)