MATHEMATICAL MODELLING OF INTERNAL HIV DYNAMICS

We study a mathematical model for the viral dynamics of HIV in an infected individual in the presence of HAART. The paper starts with a literature review and then formulates the basic mathematical model. An expression for R-0, the basic reproduction number of the virus under steady state application of HAART, is derived followed by an equilibrium and stability analysis. There is always a disease-free equilibrium (DFE) which is globally asymptotically stable for R-0<1. Deterministic simulations with realistic parameter values give additional insight into the model behaviour. We then look at a stochastic version of this model and calculate the probability of extinction of the virus near the DFE if initially there are only a small number of infected cells and infective virus particles. If R-0 <= 1 then the system will always approach the DFE, where as if R-0>1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R-0>1 those which do not die out approach a stochastic quasi-equilibrium consisting of random fluctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these fluctuations is so small that practically the system is at the non-trivial equilibrium. A brief discussion concludes the paper.