Structured populations with diffusion in state space

Karl Peter Hadeler; Karl Peter Hadeler

doi:10.3934/mbe.2010.7.37

Mathematical Biosciences and Engineering

2010, Volume 7, Issue 1: 37-49. doi: 10.3934/mbe.2010.7.37

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Structured populations with diffusion in state space

Karl Peter Hadeler

1.
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287

Received: 01 May 2009 Accepted: 29 June 2018 Published: 01 January 2010
MSC : Primary: 92D25; Secondary: 35K57, 49L25.

The classical models for populations structured by size have two features which may cause problems in biologically realistic modeling approaches: the structure variable always increases, and individuals in an age cohort that are identical initially stay identical throughout their lives. Here a diffusion term is introduced in the partial differential equation which mathematically amounts to adding viscosity. This approach solves both problems but it requires to identify appropriate boundary (recruitment) conditions. The method is applied to size-structured populations, metapopulations, infectious diseases, and vector-transmitted diseases.
- population structure,
- convection diffusion equation,
- viscosity approach.,
- size distribution
Citation: Karl Peter Hadeler. Structured populations with diffusion in state space[J]. Mathematical Biosciences and Engineering, 2010, 7(1): 37-49. doi: 10.3934/mbe.2010.7.37

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Abstract

The classical models for populations structured by size have two features which may cause problems in biologically realistic modeling approaches: the structure variable always increases, and individuals in an age cohort that are identical initially stay identical throughout their lives. Here a diffusion term is introduced in the partial differential equation which mathematically amounts to adding viscosity. This approach solves both problems but it requires to identify appropriate boundary (recruitment) conditions. The method is applied to size-structured populations, metapopulations, infectious diseases, and vector-transmitted diseases.
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