A contact process with mutations on a tree

2006/12/19 by Thomas M. Liggett, Liggett, Thomas M., Rinaldo B. Schinazi +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #60K35 #Bioinformatics and Genomic Networks #Complex Network Analysis Techniques #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #math.PR #msc:60K35

paper · pdf · doi:10.48550/arxiv.math/0612564

arxiv created 2006/12/19 · openalex publication_date 2006/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the following stochastic model for immune response. Each pathogen gives birth to a new pathogen at rate λ. 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 (2006) 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.

Citations

• Spatial and non-spatial stochastic models for immune response

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• A contact process with stronger mutations on trees

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