Order reduction for an RNA virus evolution model

Andrei  Korobeinikov; Aleksei  Archibasov; Vladimir  Sobolev; Andrei  Korobeinikov; Aleksei  Archibasov; Vladimir  Sobolev

doi:10.3934/mbe.2015.12.1007

Mathematical Biosciences and Engineering

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

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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: 01 August 2014 Accepted: 29 June 2018 Published: 01 June 2015
MSC : Primary: 92D15; Secondary: 35Q92, 34E13.

A mathematical or computational model in evolutionary biologyshould necessary combine several comparatively fast processes,which actually drive natural selection and evolution, with a veryslow process of evolution. As a result, several very differenttime scales are simultaneously present in the model; this makesits analytical study an extremely difficult task. However, thesignificant difference of the time scales implies the existence ofa possibility of the model order reduction through a process oftime separation. In this paper we conduct the procedure of modelorder reduction for a reasonably simple model of RNA virusevolution reducing the original system of three integro-partialderivative equations to a single equation. Computations confirmthat there is a good fit between the results for the original andreduced models.

Keywords:

Citation: Andrei Korobeinikov, Aleksei Archibasov, Vladimir Sobolev. Order reduction for an RNA virus evolution model[J]. Mathematical Biosciences and Engineering, 2015, 12(5): 1007-1016. doi: 10.3934/mbe.2015.12.1007

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Abstract

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This article has been cited by:

1.	Anna Maria Riera-Escandell, Andrei Korobeinikov, 2019, Chapter 5, 978-3-030-25260-1, 27, 10.1007/978-3-030-25261-8_5
2.	Silvia Pagliarini, Andrei Korobeinikov, Order reduction for a model of marine bacteriophage evolution, 2017, 811, 1742-6588, 012010, 10.1088/1742-6596/811/1/012010
3.	A Numerical Method for Solving a Class of Nonlinear Second Order Fractional Volterra Integro-Differntial Type of Singularly Perturbed Problems, 2018, 6, 2227-7390, 48, 10.3390/math6040048
4.	Silvia Pagliarini, Andrei Korobeinikov, A mathematical model of marine bacteriophage evolution, 2018, 5, 2054-5703, 171661, 10.1098/rsos.171661
5.	Silvia Pagliarini, Andrei Korobeinikov, 2018, Chapter 10, 978-3-030-01152-9, 53, 10.1007/978-3-030-01153-6_10
6.	Andrei Korobeinikov, Immune response and within-host viral evolution: Immune response can accelerate evolution, 2018, 456, 00225193, 74, 10.1016/j.jtbi.2018.08.003
7.	Andrei Korobeinikov, Stefano Pedarra, 2019, Chapter 4, 978-3-030-25260-1, 19, 10.1007/978-3-030-25261-8_4
8.	Stanca M. Ciupe, Jessica M. Conway, Incorporating Intracellular Processes in Virus Dynamics Models, 2024, 12, 2076-2607, 900, 10.3390/microorganisms12050900

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