Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

Mathematical modelling of internal HIV dynamics

Dalal, Nirav and Greenhalgh, David and Mao, Xuerong and , University of Strathclyde (Funder) (2009) Mathematical modelling of internal HIV dynamics. Discrete and Continuous Dynamical Systems - Series B, 12 (2). pp. 305-321. ISSN 1531-3492

[img]
Preview
PDF (dcdsb_03(1).pdf)
Download (289Kb) | Preview

    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 disease-free 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 quasi-equilibrium consisting of random uctuations about the non-trivial deterministic equilibrium levels, but the amplitude of these uctuations is so small that practically the system is at the non-trivial 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
    Subjects: Science > Mathematics
    Department: Faculty of Science > Mathematics and Statistics
    Faculty of Science > Mathematics and Statistics > Statistics and Modelling Science
    Related URLs:
    Depositing user: Mrs Ann Lynch
    Date Deposited: 14 Jan 2010 14:13
    Last modified: 12 Mar 2012 13:57
    URI: http://strathprints.strath.ac.uk/id/eprint/14034

    Actions (login required)

    View Item

    Fulltext Downloads: