Mathematical modelling of internal HIV dynamics
Dalal, Nirav and Greenhalgh, David and Mao, Xuerong (2009) Mathematical modelling of internal HIV dynamics. Discrete and Continuous Dynamical Systems  Series B, 12 (2). pp. 305321. ISSN 15313492

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Abstract
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 R0, 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 diseasefree equilibrium (DFE) which is globally asymptotically stable for R0 < 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 R0 1 then the system will always approach the DFE, whereas if R0 > 1 then some simulations will die out whereas others will not. Stochastic simulations suggest that if R0 > 1 those which do not die out approach a stochastic quasiequilibrium consisting of random uctuations about the nontrivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the nontrivial equilibrium. A brief discussion concludes the paper.
Item type:  Article 

ID code:  14034 
Keywords:  HIV, AIDS, HAART, differential equations, R0, equilibrium and stability, analysis, deterministic model, stochastic model, probability of extinction, simulation, Mathematics, Discrete Mathematics and Combinatorics, Applied Mathematics 
Subjects:  Science > Mathematics 
Department:  Faculty of Science > Mathematics and Statistics Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science 
Depositing user:  Mrs Ann Lynch 
Date Deposited:  14 Jan 2010 14:13 
Last modified:  01 Apr 2017 08:38 
Related URLs:  
URI:  http://strathprints.strath.ac.uk/id/eprint/14034 
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