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.