|Appears in Collections:||Computing Science and Mathematics Journal Articles|
|Peer Review Status:||Refereed|
|Title:||Pathogen evolution in switching environments: A hybrid dynamical system approach|
|Authors:||Farkas, Jozsef Zoltan|
|Keywords:||Hybrid switching system|
Stability in probability
|Citation:||Farkas JZ, Hinow P & Engelstadter J (2012) Pathogen evolution in switching environments: A hybrid dynamical system approach, Mathematical Biosciences, 240 (1), pp. 70-75.|
|Abstract:||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 jump process. 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 stability in probability of monomorphic equilibria. We prove that in a "constantly" fluctuating environment, the genotype with the highest mean fitness is asymptotically stable in probability while all others are unstable in probability. However, if the probability of host switching depends on the genotype composition of the population, polymorphism can be stably maintained.|
|Rights:||The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.|
|Notes:||Publisher version attached for deposit in STORRE. Preprint made available on RMS web page.|
|Affiliation:||Mathematics - CSM Dept|
University of Wisconsin-Milwaukee
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