## Mathematical Modelling of Natural Phenomena

### Human Immunodeficiency Virus Infection : from Biological Observations to Mechanistic Mathematical Modelling

a1 Institute of Numerical Mathematics, RAS, Moscow, Russia

a2 Institute of Immunology and Physiology, Ural Branch RAS, Ekaterinburg, Russia

a3 Sobolev Institute of Mathematics, Siberian Branch RAS, Novosibirsk, Russia

a4 State Research Center of Virology and Biotechnology “Vector", Novosibirsk Region, Koltsovo, Russia

a5 Institute of Ecology and Genetics of Microorganisms, Ural Branch RAS, Perm, Russia

a6 ICREA Infection Biology Laboratory, Department of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona, Spain

Abstract

HIV infection is multi-faceted and a multi-step process. The virus-induced pathogenic mechanisms are manifold and mediated through a range of positive and negative feedback regulations of immune and physiological processes engaged in virus-host interactions. The fundamental questions towards understanding the pathogenesis of HIV infection are now shifting to ‘dynamic’ categories: (i) why is the HIV-immune response equilibrium finally disrupted? (ii) can one modify the dynamic equilibrium for host benefit? (iii) can one predict the outcome of a system perturbation via antiviral drugs or drugs modulating the host immune response dynamics? Answering these questions requires a major interdisciplinary effort, and in particular, the development of novel mathematical approaches for a coherent quantitative description and prediction of intra-patient HIV evolution, the immunological responses to HIV infection, and the systems level homeostatic regulation of specific effector and regulatory lymphocyte populations in correlation with disease status. Here we summarized fundamental biological features of HIV infection and current mathematical modelling attempts to understand HIV pathogenesis.

(Online publication October 17 2012)

Key Words:

• mathematical modelling;
• host–pathogen interaction;
• immune system;
• human immunodeficiency virus infection

Mathematics Subject Classification:

• 35Q92;
• 37N25;
• 92-02;
• 92B05;
• 92C30;
• 92C42;
• 93A30;
• 97M60

Correspondence:

c1 Corresponding author. E-mail: bocharov@inm.ras.ru

c2 Corresponding author. E-mail: andreas.meyerhans@upf.edu

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