Order reduction for an RNA virus evolution model
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 mode...
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| Format: | Article |
| Language: | English |
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AIMS Press
2015-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1007 |
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| author | Andrei Korobeinikov Aleksei Archibasov Vladimir Sobolev |
| author_facet | Andrei Korobeinikov Aleksei Archibasov Vladimir Sobolev |
| author_sort | Andrei Korobeinikov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-11fe942c7a87467584a21cc1c0226a58 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-11fe942c7a87467584a21cc1c0226a582025-01-24T02:33:19ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-05-011251007101610.3934/mbe.2015.12.1007Order reduction for an RNA virus evolution modelAndrei Korobeinikov0Aleksei Archibasov1Vladimir Sobolev2Centre de Recerca Matemática, Campus de Bellaterra, Edifici C, 08193 BarcelonaDepartment of Applied Mathematics, Samara State Aerospace University (SSAU), 443086 Samara, 34, Moskovskoye shosseDepartment of Technical Cybernetics, Samara State Aerospace University (SSAU), 443086 Samara, 34, Moskovskoye shosseA 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.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1007viral dynamicsphenotype spacebasicreproduction number.nowak--may modelsingularly perturbed systemdarwinianfitnessvariant spacehivslow-fast dynamicsviral evolutionintegro--differential equations |
| spellingShingle | Andrei Korobeinikov Aleksei Archibasov Vladimir Sobolev Order reduction for an RNA virus evolution model Mathematical Biosciences and Engineering viral dynamics phenotype space basicreproduction number. nowak--may model singularly perturbed system darwinianfitness variant space hiv slow-fast dynamics viral evolution integro--differential equations |
| title | Order reduction for an RNA virus evolution model |
| title_full | Order reduction for an RNA virus evolution model |
| title_fullStr | Order reduction for an RNA virus evolution model |
| title_full_unstemmed | Order reduction for an RNA virus evolution model |
| title_short | Order reduction for an RNA virus evolution model |
| title_sort | order reduction for an rna virus evolution model |
| topic | viral dynamics phenotype space basicreproduction number. nowak--may model singularly perturbed system darwinianfitness variant space hiv slow-fast dynamics viral evolution integro--differential equations |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.1007 |
| work_keys_str_mv | AT andreikorobeinikov orderreductionforanrnavirusevolutionmodel AT alekseiarchibasov orderreductionforanrnavirusevolutionmodel AT vladimirsobolev orderreductionforanrnavirusevolutionmodel |