Structured populations with diffusion in state space

Pages: 37 - 49, Volume 7, Issue 1, January 2010

doi:10.3934/mbe.2010.7.37       Abstract        Full Text (167.9K)       Related Articles

Karl Peter Hadeler - School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, United States (email)

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.

Keywords:  population structure, size distribution, convection diffusion equation, viscosity approach.
Mathematics Subject Classification:  Primary: 92D25; Secondary: 35K57, 49L25.

Received: May 2009;      Accepted: October 2009;      Published: January 2010.