Order reduction for an rna virus evolution model

Andrei Korobeinikov; Aleksei Archibasov; Vladimir Sobolev

doi:10.3934/mbe.2015.12.1007

Order reduction for an rna virus evolution model

Andrei Korobeinikov, Aleksei Archibasov, Vladimir Sobolev

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

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 integropartial derivative equations to a single equation. Computations confirm that there is a good fit between the results for the original and reduced models.

Original language	English
Pages (from-to)	1007-1016
Journal	Mathematical Biosciences and Engineering
Volume	12
Issue number	5
DOIs	https://doi.org/10.3934/mbe.2015.12.1007
Publication status	Published - 1 Jan 2015

Keywords

Basic reproduction number
Darwinian fitness
HIV
Integro-differential equations
Nowak-May model
Phenotype space
Singularly perturbed system
Slow-fast dynamics
Variant space
Viral dynamics
Viral evolution

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.3934/mbe.2015.12.1007

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title = "Order reduction for an rna virus evolution model",

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 integropartial derivative equations to a single equation. Computations confirm that there is a good fit between the results for the original and reduced models.",

keywords = "Basic reproduction number, Darwinian fitness, HIV, Integro-differential equations, Nowak-May model, Phenotype space, Singularly perturbed system, Slow-fast dynamics, Variant space, Viral dynamics, Viral evolution",

author = "Andrei Korobeinikov and Aleksei Archibasov and Vladimir Sobolev",

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doi = "10.3934/mbe.2015.12.1007",

language = "English",

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journal = "Mathematical Biosciences and Engineering",

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T1 - Order reduction for an rna virus evolution model

AU - Korobeinikov, Andrei

AU - Archibasov, Aleksei

AU - Sobolev, Vladimir

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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 integropartial derivative equations to a single equation. Computations confirm that there is a good fit between the results for the original and reduced models.

AB - 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 integropartial derivative equations to a single equation. Computations confirm that there is a good fit between the results for the original and reduced models.

KW - Basic reproduction number

KW - Darwinian fitness

KW - HIV

KW - Integro-differential equations

KW - Nowak-May model

KW - Phenotype space

KW - Singularly perturbed system

KW - Slow-fast dynamics

KW - Variant space

KW - Viral dynamics

KW - Viral evolution

U2 - 10.3934/mbe.2015.12.1007

DO - 10.3934/mbe.2015.12.1007

M3 - Article

VL - 12

SP - 1007

EP - 1016

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 5

ER -

Order reduction for an rna virus evolution model

Abstract

Keywords

UN SDGs

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