Pathogen evolution in switching environments: a hybrid dynamical system approach

Details Pathogen evolution in switching environments: a hybrid dynamical system approach Pathogen evolution in switching environments: a hybrid dynamical system approach

2011-04-15

arxiv.org/abs/1104.3001v1

Mathematics

Classical Analysis and ODEs

Scientific paper

We propose a hybrid dynamical system approach to model the evolution of a pathogen that experiences different selective pressures according to a stochastic process. In every environment, the evolution of the pathogen is described by a version of the Fisher-Haldane-Wright equation while the switching between environments follows a Markov process with a given generator matrix. We investigate how the qualitative behavior of a simple single-host deterministic system changes when the stochastic switching process is added. In particular, we study the exchange of stability between monomorphic equilibria. Our results are consistent with the view that in a fluctuating environment, the genotype with the highest mean fitness will eventually become fixed. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.

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