A contact process with mutations on a tree

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:118

Article

Liggett, Thomas M.³  Schinazi, Rinaldo B.²  Schweinsberg, Jason¹ 

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[2] Univ Colorado, Colorado Springs, CO 80907 USA

[3] Univ Calif Los Angeles, Los Angeles, CA USA

关键词: mutation;    immune system;    branching process;    spatial stochastic model;    contact process;   

DOI  :  10.1016/j.spa.2007.04.007

来源: Elsevier

【 摘 要 】

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate lambda. When a new pathogen is born, it has the same type as its parent with probability 1 - r. With probability r, a mutation occurs, and the new pathogen has a different type from all previously observed pathogens. When a new type appears in the population, it survives for an exponential amount of time with mean 1, independently of all the other types. All pathogens of that type are killed simultaneously. Schinazi and Schweinsberg [R.B. Schinazi, J. Schweinsberg, Spatial and non-spatial stochastic models for immune response, Markov Process. Related Fields (2006) (in press)] have shown that this model on Z(d) behaves rather differently from its non-spatial version. In this paper, we show that this model on a homogeneous tree captures features from both the non-spatial version and the Z(d) version. We also obtain comparison results, between this model and the basic contact process on general graphs. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

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