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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 784512, 17 pages
http://dx.doi.org/10.1155/2012/784512
Research Article

Immune Response to a Variable Pathogen: A Stochastic Model with Two Interlocked Darwinian Entities

Biomedical Optics Research Laboratory, Clinic of Neonatology, University Hospital Zürich, Frauenklinikstrasse 10, CH-8091 Zürich, Switzerland

Received 4 January 2012; Revised 13 April 2012; Accepted 28 June 2012

Academic Editor: Zvia Agur

Copyright © 2012 Christoph Kuhn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents the modeling of a host immune system, more precisely the immune effector cell and immune memory cell population, and its interaction with an invading pathogen population. It will tackle two issues of interest; on the one hand, in defining a stochastic model accounting for the inherent nature of organisms in population dynamics, namely multiplication with mutation and selection; on the other hand, in providing a description of pathogens that may vary their antigens through mutations during infection of the host. Unlike most of the literature, which models the dynamics with first-order differential equations, this paper proposes a Galton-Watson type branching process to describe stochastically by whole distributions the population dynamics of pathogens and immune cells. In the first model case, the pathogen of a given type is either eradicated or shows oscillatory chronic response. In the second model case, the pathogen shows variational behavior changing its antigen resulting in a prolonged immune reaction.