Order reduction for an RNA virus evolution model

Andrei  Korobeinikov; Aleksei  Archibasov; Vladimir  Sobolev

doi:10.3934/mbe.2015.12.1007

Article Contents

2015, Volume 12, Issue 5: 1007-1016. Doi: 10.3934/mbe.2015.12.1007

This issue Previous Article Multi-host transmission dynamics of schistosomiasis and its optimal control Next Article Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering

Order reduction for an RNA virus evolution model

1.
Centre de Recerca Matemática, Campus de Bellaterra, Edifici C, 08193 Barcelona
2.
Department of Applied Mathematics, Samara State Aerospace University (SSAU), 443086 Samara, 34, Moskovskoye shosse
3.
Department of Technical Cybernetics, Samara State Aerospace University (SSAU), 443086 Samara, 34, Moskovskoye shosse

Received: July 31, 2014

Revised: March 31, 2015

Published: May 2015

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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.

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Mathematics Subject Classification: Primary: 92D15; Secondary: 35Q92, 34E13.

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