Evolving pathogen phylogenies: a two-level branching approach

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For many RNA viruses the lack of a proofreading mechanism in the virus' RNA polymerase results in frequent mutation. The high viral mutation rates, the large virus population size, and the short replication periods produce abundance of viral variability which is responsible for immune escape or drug resistance Understanding in detail the forces which maintain this diversity can assist in the struggle against viral infections. Pathogen patterns - and in particular the shapes of the phylogenies - are affected by the strength of selective pressure due to various levels of cross-immunity. We focus on the temporal structure of phylogenies associated with a persistent virus. We propose a two-level (host-pathogen) branching model with mutation and competition on both levels in different scaling regimes, where hosts can be either the infected patients or the infected cells within a single patient.We thereby extend our recent work on a panmitic virus population. We will further rely on techniques developed for measure-valued (neutral) multilevel branching dynamics and two-level multi-type branching dynamics with mutation and competition.