Abstract
A mathematical or computational model in evolutionary biology should necessary combine several comparatively fast processes, which actually drive natural selection and evolution, with a very slow process of evolution. As a result, several very different time scales are simultaneously present in the model; this makes its analytical study an extremely difficult task. However, the significant difference of the time scales implies the existence of a possibility of the model order reduction through a process of time separation. In this paper we conduct the procedure of model order reduction for a reasonably simple model of RNA virus evolution reducing the original system of three integro-partial derivative equations to a single equation. Computations confirm that there is a good fit between the results for the original and reduced models.
Highlights
Due to very high mutation and replication rates combined with high recombination abilities, RNA viruses are able to evolve very fast
The development of mathematical or computational models of viral evolution which can be used in combination with experimental studies in evolutionary biology, remains a challenge even for such a simple object as RNA virus
A combination of several time scales within a model suggests that such a model can be significantly simplified using the scale separation techniques
Summary
Due to very high mutation and replication rates combined with high recombination abilities, RNA viruses are able to evolve very fast. This mechanistic model is an extension of Nowak–May HIV model [6], where viral phenotypes (strains) are assumed to be distributed in a continuous phenotype space, and random mutations are described by dispersion.
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