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Report on the mini-symposium on Nonlinear Population Dynamics

This mini-symposium was part of the conference Theory and Mathematics in Biology and Medicine 1999 Vrije Universiteit Amsterdam, The Netherlands, June 29 - July 3, 1999.

This mini-symposium was announced in the continuation research proposal for NLS Population dynamics and epidemics financially supported by the NWO priority program `Nonlinear Systems, Population dynamics, including epidemiology'. Sessions organizers were Martin Boer (VU now CPRO, Wageningen) and Markus. Kirkilonis (CWI, UU and now Heidelberg Germany). The reseach projects of Martin ( Ph.D. student Dept. of Theoretical Biology VU) and Markus (post-doc with the CWI) were supported by the NLS priority program. Martin Boer is finishing his Ph.D. thesis entitled: The dynamics of tri-trophic food chains. Markus was involved in the development of theory and numerical bifurcation analysis of models of physiologically structured populations. To that end he wrote the computer package called BASE, a modularly designed tool for 'Bifurcation Analysis of Structured Equations'.

Two invited speakers gave a rather broad introduction into the scientific field of nonlinear population dynamics. In parallel sessions oral contributions were presented. Furthermore there was a well attended poster-session.

Abstracts of the contributions of the invited speakers:

David Rand, University of Warwick, Mathematics Institute, Coventry CV4 7AL UK

In this talk I propose to discuss population dynamics with a particular emphasis on recent trends and future perspectives. In the first part I will concentrate on ecology, evolutionary theory and epidemiology and my discussion will include individual-based systems, spatial ecologies, populations of structured individuals and invasion. In the second part I want to consider some examples from microbial and molecular biology such as viral systems, T-cell receptors and cell signalling. On the one hand I want to demonstrate that population dynamics is crucial to an understanding of many biological phenomena of real current interest and on the other hand I want to draw attention to the way in which new mathematical techniques can aid understanding of population dynamics.

Hal Smith, Arizona State University, Mathematics, Tempe, AZ 85287, USA
e-mail: Coauthor(s): Mary Ballyk, Don Jones

A mathematical model for microbial growth and competition for limiting nutrient and for limited wall attachment sites in a plug flow reactor will be presented. The model is an adaptation of a model, due to Rolf Freter for cstr, to examine the effect of wall attachment of bacteria in the mammalian gut on the stability of the natural microflora of the gut to invasion. We will present both analytical and numerical results which bear on such questions as 'for what gut residence times and cell doubling times can the bacteria persist?', 'how can many strains coexist in the gut?' 'when does a potential invader have a competitive edge over a resident strain?'.

All abstracts are still available on:
The oral presentations:

Poster contributions:

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Next: Report of visit of Up: nls-99-3.html Previous: Report on Workshop on

Bob Kooi
Fri Nov 12 21:13:40 MET 1999