Intra-Host stochastic models for HIV dynamics and management Thesis uri icon


  • Mathematical models can facilitate the understanding of complex dynamics of many biomedical systems such as epidemiology, ecology and virology. The main objective of this study was to make use of mathematical models, this sought to develop and use stochastic modeling to model HIV dynamics and its management. Mathematical models can help to improve our understanding of dynamics of diseases such as in HIV/AIDS by providing an alternative way to study the effects of different drugs, a procedure which is otherwise risky or unethical when carried out on patients. Untangling the dynamics between HIV and CD+ 4 cellular populations and molecular interactions can be used to investigate the effective points of interventions in the HIV life cycle. Many existing models on within-Host HIV dynamics make simplifying assumptions concerning the HIV targeted immune cells by assuming that the virus only affects CD+ 4 cells. However, other immune cells play also important roles in HIV progression. Also the deterministic models lack the effect of randomness,hence stochastic models are developed which are used to capture the dynamics of HIV infection and examine various alternatives for the control and treatment of the virus. The HIV and AIDS epidemic is extremely dynamic; this dynamism orthogonally complicates interventions embraced for the management of the epidemic. This study was firstly motivated by the fact that eradication of the HIV virus is not attainable with the current available drugs and the focus has now shifted from eradication of the virus to the management and control of the virus’ progression. Secondly, the treatment of HIV is expensive and often times erratic. It is therefore necessary to develop a mathematical model which when applied to HIV data accurately details the cost of treating a HIV patient. Stochastic models are formulated which describe the interaction of HIV, langerhans cells (LCs) and the CD+ 4 cells. Difference differential equations are obtained and solved using probability generating function to obtain moments of the numbers of uninfected immune cells, the HIV infected CD+ 4 T cells, and the free HIV particles at any time t. The model analysis showed that, eradication of HIV is not possible without clearance of latently infected langerhans cells and the predicted rate of decline in plasma HIV virus concentration depends on three factors: the death rate of the virons, the efficacy of therapy and the length of the intracellular delay. The model produces interesting feature that successfully treated HIV patients will have low, undetectable viral load. Stochastic models based on Semi-Markov process were formulated describing the progression of HIV in an infected person. Firstly, Internal transition probabilities were computed, which capture the probability of survival for the HIV patient under treatment. It will also show the effects of covariates:- age, follow up time and initial state on the disease progression. Secondly, a model for the cost of treating a HIV patient was formulated. This model captures the cost of managing a HIV patient given the starting state and the treatment combination which is most effective at each disease state. Lastly, a Treatment Reward Model (TRM) was formulated, which gave insights on the state, which the patient should be maintained so that they remain healthy, productive, and non-infectious, and also the optimal or effective time to initiate HIV therapy.

publication date

  • November 2013

number of pages

  • 197