Talk abstract:

Hyperbolic v Parabolic Models for Chemotaxis (Individual and Population Density Based Models)

Angela Stevens
Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26
D-04103 Leipzig
Germany
stevens@mis.mpg.de

To get an insight into aggregation phenomena and/or selforganization in microbiology, one often measures the speed and the turning frequencies of the individuals of the respective species and then tries to find out about dependencies of these parameters, e.g. on the species itself or on other agents. Mathematical modeling takes these measurements into account and then addresses the question, whether these assumptions do account for aggregation of the total population or not.

In this talk several individual and population density based models for chemotactic movement are discussed and compared with each other with respect to their aggregation effect. Among them are hyperbolic models for chemotaxis, which include information about the speed and turning frequency of the population, the classical Keller-Segel model, which is formulated in terms of the diffusion and chemotactic sensitivity of the population, discrete single particle jump processes, which again are based on the speed and turning frequency, and continuous many particle models, which combine Brownian motion of each individual and their chemotactic drift.

Part of this talk is joint work with Thomas Hillen.

Reference:

Hillen T. and Stevens A. (1999): Hyperbolic Models for Chemotaxis in 1D. Accepted in Journal of Nonlinear Analysis: Theory, Methods and Applications Series B.

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1998-1999 Mathematics in Biology