American Institute of Mathematical Sciences

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2010, 7(1): 37-49. doi: 10.3934/mbe.2010.7.37

Structured populations with diffusion in state space

Karl Peter Hadeler 1,

1. 

School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States

Received  May 2009 Revised  October 2009 Published  January 2010

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.
Keywords: population structure, convection diffusion equation, viscosity approach., size distribution.
Mathematics Subject Classification: Primary: 92D25; Secondary: 35K57, 49L2.
Citation: Karl Peter Hadeler. Structured populations with diffusion in state space. Mathematical Biosciences & Engineering, 2010, 7 (1) : 37-49. doi: 10.3934/mbe.2010.7.37
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