Structured populations with diffusion in state space
The classical models for populationsstructured by size have two features which may cause problems inbiologically realistic modeling approaches: the structure variablealways increases, and individuals in an age cohort that areidentical initially stay identical throughout their lives. Here adiffusion...
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| Format: | Article |
| Language: | English |
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AIMS Press
2009-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.37 |
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| _version_ | 1832590223041626112 |
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| author | Karl Peter Hadeler |
| author_facet | Karl Peter Hadeler |
| author_sort | Karl Peter Hadeler |
| collection | DOAJ |
| description | The classical models for populationsstructured by size have two features which may cause problems inbiologically realistic modeling approaches: the structure variablealways increases, and individuals in an age cohort that areidentical initially stay identical throughout their lives. Here adiffusion term is introduced in the partial differential equationwhich mathematically amounts to adding viscosity. This approachsolves both problems but it requires to identify appropriateboundary (recruitment) conditions. The method is applied tosize-structured populations, metapopulations, infectious diseases, and vector-transmitted diseases. |
| format | Article |
| id | doaj-art-dd64b2d4cddd4730b9adf198627d9301 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-dd64b2d4cddd4730b9adf198627d93012025-01-24T02:00:16ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-12-0171374910.3934/mbe.2010.7.37Structured populations with diffusion in state spaceKarl Peter Hadeler0School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287The classical models for populationsstructured by size have two features which may cause problems inbiologically realistic modeling approaches: the structure variablealways increases, and individuals in an age cohort that areidentical initially stay identical throughout their lives. Here adiffusion term is introduced in the partial differential equationwhich mathematically amounts to adding viscosity. This approachsolves both problems but it requires to identify appropriateboundary (recruitment) conditions. The method is applied tosize-structured populations, metapopulations, infectious diseases, and vector-transmitted diseases.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.37population structureconvection diffusion equationviscosity approach.size distribution |
| spellingShingle | Karl Peter Hadeler Structured populations with diffusion in state space Mathematical Biosciences and Engineering population structure convection diffusion equation viscosity approach. size distribution |
| title | Structured populations with diffusion in state space |
| title_full | Structured populations with diffusion in state space |
| title_fullStr | Structured populations with diffusion in state space |
| title_full_unstemmed | Structured populations with diffusion in state space |
| title_short | Structured populations with diffusion in state space |
| title_sort | structured populations with diffusion in state space |
| topic | population structure convection diffusion equation viscosity approach. size distribution |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.37 |
| work_keys_str_mv | AT karlpeterhadeler structuredpopulationswithdiffusioninstatespace |