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September  2009, 12(2): 305-321. doi: 10.3934/dcdsb.2009.12.305

Mathematical modelling of internal HIV dynamics

Nirav Dalal 1, , David Greenhalgh 1, and  Xuerong Mao 1,

1. 

Department of Statistics and Modelling Science, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, United Kingdom, United Kingdom

Received  October 2008 Revised  April 2009 Published  July 2009

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.
Keywords: equilibrium and stability analysis, HAART, differential equations, simulation., stochastic model, deterministic model, AIDS, probability of extinction, HIV, $R_0$.
Mathematics Subject Classification: Primary: 92B05, 92D25; Secondary: 34D23, 60J85, 92D3.
Citation: Nirav Dalal, David Greenhalgh, Xuerong Mao. Mathematical modelling of internal HIV dynamics. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 305-321. doi: 10.3934/dcdsb.2009.12.305
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