Mathematical modelling of internal HIV dynamics

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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

Abstract
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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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