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A contact process with mutations on a tree. (English) Zbl 1141.60065
Here the authors study evolution of the following branching process: a 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 \(1-r\). The new pathogen has a different type with probability \(r\). A new type survives for an exponential amount of time with mean 1. All pathogens of that type are killed simultaneously. The authors show that this model for immune response captures features from spatial and non-spatial versions. Conditions on \(\lambda\) and \(r\) under which the process dies or survives are obtained.

60K35 Interacting random processes; statistical mechanics type models; percolation theory
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