A newsletter for the project ‘Population dynamics, including epidemiology’ being part of the NWO priority program ‘Nonlinear Systems’.

October 1, 1998

Visit the Home Page on:

http://www.bio.vu.nl/thb/users/nls

This newsletter will appear once every three months during the course of the project. Its content will mainly consist of announcements of activities, such as seminars and workshops. Moreover, information about foreign visitors being in the Netherlands as part of the program will be given.

To make this newsletter as informative as possible we ask you to let us know about activities that are planned and the date visitors are coming and give lectures. Also addresses of persons (in the Netherlands or abroad) who might be interested in receiving this newsletter are welcome.

All correspondence should be sent to: Bob Kooi

Theoretical Biology Vrije Universiteit De Boelelaan 1087 1081 HV Amsterdam

                                                   Email: kooi@bio.vu.nl

Contents

1 Editorial 2

2 Proposals 1998-1999 3 2.1 Modelling of contact structure and the spread of infectious diseases . . . . . . 3 2.2 Bioinformatics: pursuing opportunities in the Netherlands . . . . . . . . . . . 4

3 The milker-killer dilemma in Utrecht and Tübingen 6

4 Report of visit prof. Sergio Rinaldi 6

5 Calendar 8

Contributions to this newsletter were made by: Odo Diekmann,Thomas Hantke, R.C. Jansen, Bob Kooi, Mirjam Kretzschmar.

1 Editorial

The URL of the home-page for the NLS Population Dynamics and Epidemiology project is: http://www.bio.vu.nl/thb/users/nls Activities of the programme as well as useful links are given in a Calendar. You can down-load from this home-page the Newsletter (4 issues per year) in PostScript and DVI format. For the time being the newsletter will also be send by ordinary mail.

This home-page will be updated four times a year when also the new newsletter is issued. Only the calendar is updated more frequently. Please do not hesitate to contact for updates, improvements, suggestions and so on.

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to Karin Uyldert, Vrije Universiteit, de Boelelaan 1087, 1081 HV, Amsterdam or email:

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2 Proposals 1998-1999

Descriptions of the two granted proposals:

2.1 Modelling of contact structure and the spread of infectious diseases

Principal organiser: Dr. Mirjam Kretzschmar, Other participating groups: Dr. Mart C.M. de Jong Epidemiology, Statistics & Modelling ID-DLO P.O. Box 65 8200 AB Lelystad

Activity: one/two-day workshop The workshop was organized already on September 24, 1998. Names of proposed speakers: Lisa Sattenspiel (University of Missouri, USA), Minus van Baalen (UvA), Mart de Jong (ID-DLO), Matt Keeling (Cambridge University, UK), Gianpaolo Scalia-Tomba (Universita La Sapienza, Rome, Italy), Klaus Dietz (University of Tübingen, Germany), Tom Snijders (RUG), John Edmunds (University of Warwick), Jacco Wallinga (RIVM), Nico Nagelkerke (RIVM & KNCV).

Motivation: Models for the spread of infectious diseases are inherently non-linear, because transmission takes place when two individuals of a population interact in a way that enables the pathogen to spread from an infectious to a susceptible host. In the simplest epidemic models the term describing the interaction or contact between two individuals is a quadratic term based on the assumption of homogeneous mixing and mass action. The correct application of mass-action is not that straightforward because it has to be decided whether constant parameters are assumed for the model in with variables representing densities (fractions) or numbers. Moreover, it is clear that for virtually all infectious diseases and especially in human populations, the mass-action assumption is oversimplifying and one would like to have a more refined description of the contact process. One would like to know what the effects are of different contact patterns in a population on the way an infectious disease spreads and on the effectiveness of prevention measures.

Different ways to model contact structure have been discussed extensively in the last 20 years, mainly in relation with the spread of HIV/AIDS and other sexually transmitted diseases. Recently, new approaches have also been developed in the context of childhood diseases such as measles. There have been a number of papers devoted to so-called household models or epidemics with two levels of spread: local spread within small groups and global spread between those households. Similar types of models are also important for studying the spread of infections in animal populations especially in farmed animals where a division between spread within the farm and between farms seems natural. Furthermore, there have been developments in applying the so-called ’pair-approximation’ method to the classical SIR-model. On the side of empirical research there have been attempts to uncover the contact patterns underlying disease transmission in more detail, both for human diseases by sociological studies as in the veterinary context by experiments and observational studies.

The aim of the workshop is to bring together researchers who have worked on different approaches in modelling contact patterns, epidemiologists who have studied actual contact patterns in specific populations, and modellers who are applying epidemic models to public health and veterinary questions. The choice of speakers has been motivated by the idea to have representatives for each of those aspects. The date of the workshop was chosen such that it overlaps with a visit of Prof. S. Sattenspiel (Missouri) to the RIVM. Sattenspiel has worked on the spread of infectious diseases among and between groups, e.g. the spread of hepatitis A in and between day care centers, and the spread of influenza as a consequence of human mobility between different geographical regions in and among different villages of an island population. As a speaker about representative for household models we would like to invite Prof. K. Dietz (Tübingen) or G. Scalia-Tomba (Rome). Dr. M.C.M. de Jong (Lelystad) has worked on models with fixed acquaintance structure. That work is again closely related to the ’pair approximation’ approach that has been applied to the SIR-model by Dr. M. Keeling (Cambridge). Dr. M. van Baalen (Amsterdam) has investigated questions of evolution of virulence on contact networks. Dr. J. Edmunds (Warwick) has conducted an interesting pilot study about contact patterns among university students. As social processes leading to contacts between individuals in a human society are very complex, we also thought it interesting to include some aspects of sociological theory into the discussion. We therefore would like to invite Dr. T. Snijders (Groningen) who has worked on stochastic models modelling social networks in the context of sociology. Dr. N. Nagelkerke has worked on the molecular epidemiology of tuberculosis in the Netherlands and has analysed contact pattern between different ethnic groups on the basis of DNA fingerprinting of TB isolates. J. Wallinga is working on problems concerning the modelling of contact structure and the analysis of vaccination programs for childhood diseases. The workshop is planned as a one-day event, but as foreign speakers will have to stay overnight anyway, we anticipate the opportunity to have additional discussions in smaller groups on the following day.

Apart from the benefit of discussion among researchers who have contributed in one or the other way to this field of research, we hope to make those new approaches workable for mathematical modellers who are applying models to study and solve problems in public health. Those are problems concerned with the interpretation of epidemiological data, with the effectiveness of various prevention measures, and with possible long term effects of prevention such as the evolution of new strains of pathogen under the influence of public health measures. A good understanding of contact patterns and their effects on the spread of infectious diseases is paramount for those aims.

Dr. Mirjam Kretzschmar RIVM, Centre for Infectious Diseases, Epidemiology P.O. Box 1, 3720 BA Bilthoven Tel.: 030-2743749 Fax: 030-2744409 e-mail: mirjam.kretzschmar@

rivm.nl

2.2 Bioinformatics: pursuing opportunities in the Netherlands

Aanvrager: Dr R.C. Jansen

Activiteit: Voorstel voortweedaags symposium april 1999. Bioinformatica is een betrekkelijk jonge veelbelovende discipline, die in zowel de Verenigde Staten als in West-Europa een stormachtige ontwikkeling doormaakt. De oorzaak ligt in de groei van de mogelijkheden met computers, databases en Internet en in de snelle ontwikkeling van biotechnologische methoden om databases met gegevens te vullen. In vergelijking met andere landen schiet in Nederland de ontwikkeling van infrastructuur en analyse methoden te kort om de schaalvergroting van biotechnologische datastromen adequaat aan te kunnen. De vakgroep Bioinformatica (RUU; prof Hogeweg) en CAOS/CAMM (KUN, dr Nordik) zijn momenteel de belangrijkste universitaire expertisehouders binnen Nederland. Op diverse plaatsen groeit het besef dat een stevige impuls nodig is en er ontstaan dan ook initiatieven in de ontwikkeling van bioinformatica (bijv. binnen Wageningen).

Doel van het symposium is de Nederlandse bioinformatica een flinke stap vooruit te helpen.

In de literatuur wordt doorgaans de volgende omschrijving/definitie van Bioinformatica gegeven:

Multidisciplinary scientific discipline that embraces all aspects of data acquisition, distribution, management, processing and interpretation of bioscientific and biotechnological data.

Bioinformatics: a new scientific multidisciplinary scientific discipline at the interface of life sciences, mathematics and information/communcation technology, and is about capturing biological information and manipulating it into useful knowledge

Uitgangspunt is een tweedaags symposium met een duidelijk verschillend karakter op dag 1 en dag 2. Bioinformatica is een wetenschappelijke discipline die vooral wordt gedreven vanuit (multidisciplinaire) researchproblemen.

Het integreren van data en informatie uit verschillende toepassingsvelden (bijvoorbeeld biochemie, evolutie biologie, moleculaire biologie, populatie biologie, theoretische biologie, farmacie, epidemiologie, medische wetenschappen, veredeling en fokkerij) is een van de belangrijkste strategische voordelen van moderne bioinformatica. Bioinformatics is dus veel en veel meer dan bijv. DNA en eiwit sequentie analyses, alignments en structuurvalidatie. Bioinformatica vereist in belangrijke mate integratie van de genoemde toepassingsgebieden met de disciplines informatica, wiskunde en statistiek.

De opzet van symposium is also volgt: (dag 1) Bioinformatics vanuit een ‘problem driven context’, (dag 2) Bioinformatics vanuit de state-of-the-art ‘expertises’. Uitdaging is om dag 1 en dag 2 naadloos op elkaar te laten aansluiten.

Nadruk op dag 1 ligt vooral op HOE en WAAROM ‘bioinformatics tools’ worden gebruikt voor het oplossen van zowel academisch als industrile ‘multidisciplinaire’ researchproblemen. De ‘problemen’ zullen zoveel mogelijk een afspiegeling zijn van de wetenschappelijke en industrile activiteiten in Nederland [toepassingen binnen chemisch, genetisch, biologisch en medisch wetenschappelijk onderzoek; toepassingen binnen industrie, bijvoorbeeld ”new bioingredients & bioprocesses” (biotechnogische bedrijven bijv. Genecor)); ”drug target identification” (farmaceuten, bijv. Organon), ”health & functional foods” (voedingsmiddelen industrie; bv Nutrica, Unilever) en zaadveredelings- en veefokkerijbedrijven; bijv. Advanta, KeyGene, Nutreco)].

Op dag 2 zullen vooral onderliggende ‘bioinformatics technieken en wetenschappelijke expertises’ belicht worden. Dus de ‘tools’ die gebruikt worden in de behandelde ‘problemdriven’ Bioinformatics voorbeelden van dag 1. Dag 2 is dus vooral WAT wordt er gebruikt en gaat over de stand van de huidige Bioinformaticatechnologie.

Lezingen op zowel dag 1 als 2 hebben een wetenschappelijk karakter, geven vooral een overzicht. We gaan ervan uit dat het gemiddelde publiek een beperkte deskundigheid heeft zowel in het Bioinformatics vakgebied als in de vakgebieden waarin Bioinformatics wordt toegepast. We willen ze dus vooral voorlichten en inspireren (dus geen lezingen van experts voor experts). Het doel is dan ook, zeker op dag 1, een breed publiek aan te trekken dat een afspiegeling is van de relevante wetenschappelijke en industrile gebieden.

Beide dagen moeten zeker ook uitdagend werken voor informatici, wiskundigen en statistici die al dan niet al werkzaam zijn in biologische toepassingen (bijv. Populatie of Theoretische Biologie; Epidemiologie). Non-linear tools worden wel in de vakgroep Bioinformatica RUU maar momenteel nauwelijks elders gebruikt voor Bioinformatische vraagstellingen. Meer gerichte benutting van de expertise die op dit terrein in Nederland aanwezig is absoluut een niche in het Bioinformatica onderzoek. Duidelijk is dat Nederland nog verder gemobiliseerd moet worden op dit Bioinformatica terrein. Opmerkelijk is een iniatief in Cambridge (UK): najaar 1998 vindt middels workshops en themaweken gedurende een half jaar gericht onderzoek plaats naar nieuwe mathematische en statistische wegen in het Bioformatica onderzoek op het Isaac Newton Mathematical Institute.

Het forum aan het einde van dag 1 is bedoeld om de discussie tussen wetenschap, bedrijfsleven, overheid en financieringsinstellingen tot een punt te brengen waar nut en noodzaak vertaald worden tot concrete speerpunten en gerichte acties om Nederland op de mondiale Bioinformatica kaart te zetten.

Wetenschappelijk committee: Prof Borst (Nederlands Kanker Instituut), Prof Buys (RUG), Prof Hogeweg (RUU), Lee (Unilever), Muller (Organon) and Prof Veerman (Wageningen URC).

Organisatie: Dr J. Leunissen en Dr J. Nordik National Centre CAOS/CAMM for Computer Aided Chemistry and Bioinformatics, KUN PO Box 9010, 6500 GL Nijmegen, Nederland Tel. 024-3652137/3653386, Dr J de Vlieg Unilever Research Laboratorium Vlaardingen Dr R.C. Jansen en Dr J. Sandbrink Centre for Plant Breeding and Reproduction Research (CPRO-DLO) PO Box 16, 6700 AA Wageningen, Nederland Tel. 0317-477225 email: R.C.

JANSEN@CPRO.DLO.NL

3 The milker-killer dilemma in Utrecht and Tübingen

A report by Thomas Hantke. During his stay at Utrecht University (August 30 - September 4), Johannes Müller (University of Tübingen, financed by NLS) and Thomas Hantke (RIVM Bilthoven, formerly CWI) have been working together on the dynamics of a model-setup of uniformly coupled patches. This model aims to provide a tool to study the ‘milker-killer dilemma’ in a deterministic setting.

While the system of one patch already shows complicated dynamics, they investigated the dynamics of a system of two patches of equal size. They showed that, via a pitchfork bifurcation, the synchronous solution of two patches loses stability and asynchronous solutions appear.

They developed methods to continue the stable and unstable solutions numerically. By identifying parameter ranges for synchronisticallity it is possible to extend conclusions derived analytically for a one-patch system. Numerical experiments show clustering of patches to synchronous solutions. Hereby one can significantly reduce the dimensionality of the system.

As a follow-up of this cooperation, Thomas Hantke visited Johannes Müller in Tübingen in the period of 14–17 September 1998.

4 Report of visit prof. Sergio Rinaldi

Prof. Sergio Rinaldi (Politecnico di Milano, Italy) visited the Vrije Universiteit Amsterdam, June 16–18 1998, reported by Bob Kooi.

During his stay with the Theoretical Biology group Sergio discussed problems of common interest: the food chain dynamics Martin Boer is finishing his PhD-thesis on this subject. Sergio links nonlinear dynamics with (more classical) control theory and showed us that often more insight can be gained from this point of view.

On June 17 1998 there was a Mini-symposium on ‘Population Dynamics’ with five lectures: Sergio Rinaldi, Bob Kooi, Peter de Ruiter, Anje-Margriet Neutel and Hugo van den Berg. The summaries of the talks were given in the previous Newsletter May 15, 1998. One reference given in Rinaldi’s summary was incomplete, it should be: A. Gragnani, O. De Feo, and S. Rinaldi. ”Food chains in the chemostat: relationships between mean yield and complex dynamics”, Bulletin of Mathematical Biology, 60, 703–719, 1998. Martin Boer was unable to give his talk entitled: ”The dynamics of tri-trophic food chains”. A talk was given by Bob Kooi.

The summary of the talk by Bob Kooi: Food chains in the chemostat

A class of bioenergetic ecological models is studied for the dynamics of food chains with a nutrient at the base. A constant influx rate of the nutrient and a constant efflux rate for all trophic levels is assumed. Starting point is a simple model where prey is converted into predator with a fixed efficiency. This model is extended by the introduction of maintenance and energy reserves at all trophic levels, with two state variables for each trophic level, biomass and reserve energy. Then the dynamics of each population is described by two ordinary differential equations. For all models the bifurcation diagram for the bi-trophic food chain is simple. There are three important regions; a region where the predator goes to extinction, a region where there is a stable equilibrium and a region where a stable limit cycle exists. Bifurcation diagrams for tri-trophic food chains are more complicated. Flip bifurcation curves mark regions where complex dynamic behaviour (higher periodic limit cycles as well as chaotic attractors) can occur. We show numerically that Shil’nikov homoclinic orbits to saddle-focus equilibria exists. The codimension 1 continuations of these orbits form a ’skeleton’ for a cascade of flip and tangent bifurcations. The bifurcation analysis facilitates the study of the consequences of the population model for the dynamic behaviour of a food chain and invasion of a top predator into a food chain in a chemostat. Although the predicted transient dynamics of a food chain may depend sensitively on the underlying model for the populations, the global picture of the bifurcation diagram for the different models is about the same.

We investigate invasion by studying the long-term behaviour after introduction of a small amount of top predator. To that end we look at the stability of the boundary attractors; equilibria, limit cycles as well as chaotic attractors using bifurcation analysis. It will be shown that the invasibility criterion is the positiveness of the Lyapunov exponent associated with the change of the biomass of the top predator. It appears that the region in the control parameter space where a predator can invade increases with its growth rate. The resulting system becomes more resistant to further invasion when the top predator grows faster. This implies that short food chains with moderate growth rate of the top predator are liable to be invaded by fast growing invaders which consume the top predator. There may be, however, biological constraints on the top predator’s growth rate. Predators are generally larger than prey while larger organisms commonly grow slower. As a result, the growth rate generally decreases with the trophic level. This may enable short food chains to be resistant to invaders. We will relate these results to ecological community assembly and the debate on the length of food chains in nature.

Reference papers: Kooi, B.W. and Boer, M.P. and Kooijman, S.A.L.M. ”Consequences of population models on the dynamics of food chains”, Mathematical Biosciences, 153(2), 99-124, 1998.

Kooi, B.W. and Boer, M.P. and Kooijman, S.A.L.M. ”Resistance of a food chain to invasion by a top predator”, Mathematical Biosciences, accepted 1998.

The first two lectures on food chains, dealing with relatively simple models and complex dynamic behaviour, were more or less theoretically orientated. On the other hand, the last three lectures on complex food webs with a very simple model structure dealt with more practically problems and relationships with experimental data. In these food web models a linear functional response is assumed and this yields simple criteria for existence and stability of equilibria. We can conclude that there is still a large gap between theory and practice. The theme of the mini-symposium was in accordance with the renewed spirit of our NLSprogramme, that is, to broaden the group of biologists that could benefit from the activities of the programme. The lectures were appreciated and the discussions were very lively. In summary, this visit was worthwhile.

5 Calendar

June 6 and June 19, 1999

First Announcement: Mathematics in Cell Physiology and Proliferation.

In the same spirit and hopefully with the same success as the First Summer School, which took place in St. Flour (France 1997), a Second Summer School of Mathematical Biology will take place in Termoli (CB, Italy) between June 6 and June 19, 1999.

The subject of the school will be mathematical methods applied to the study of cell and molecular biology. The goal of the school is to offer doctoral students and young postdoctoral researchers a presentation of some mathematical techniques widely used in modelling problems in cell physiology and proliferation, together with a review of a selection of some such problems of contemporary relevance. The target audience is mainly composed of advanced graduate students and post- graduates in the life sciences and in mathematical disciplines (math, applied math, physics, engineering).

Classes: Duration of the school is two weeks, including 10 days of classes, Monday through Friday. Each day there will be 8 lecture units of 40 min by the staff and by invited speakers, practice sessions and lectures contributed by participants. The afternoon sessions on Tuesdays and Thursdays will be carried out at the Mario Negri Pharmacological Research Institute (Consorzio Mario Negri Sud, Santa Maria Imbaro, Chieti), the purpose being to expose the participants of the school to real-life biological problems voiced in discussions with the Mario Negri researchers.

The language of the school is English. Most school activities will take place in the same hotel where rooms and meals are provided. Most of the lecture sequences will be completed in a single week, biological subjects being treated in the first week and more theoretical subjects being treated in the second week. Bound collected notes will be provided to the school participants upon arrival to the school venue.

The number of participants is limited to 60. Interested biological and mathematical researchers, PhD students and postdoctoral fellows are encouraged to apply. While the registration fee is fixed, accomodation costs will be assessed on the basis of effective stay. The foreseen average cost of the school to participants, on the basis of the presently expected funding by institutional sponsors, is of the order of 800 Euro (double room, 15 days, full board and lodging, registration and social programme included). The organizing committee is actively seeking more funding in order to further substantially reduce the cost to participants.

An updated description of the school may be found at the web page http://space. tin.it/scienza/hjcas/biomasch.htm For all email communications please use the address

biomath@tin.it

Calendar: September 1998: First announcement, topics covered February,15 1999: Second announcement, program and logistics May 1, 1999: Deadline for submission of lecture notes and contributed presentations May 20, 1999: Deadline for pre-registration. Sunday June 6, 1999: Welcome and registration. Monday June 7 , 1999: School starts Friday June 19, 1999: School ends Saturday June 20, 1999: Farewell breakfast, speakers’ meeting.

Scientific Committee: Z. Agur (Israel), O. Arino (France, President), A. De Gaetano(Italy), M.B. Donati(Italy), A. Gandolfi(Italy), M.Kimmel(USA), M. Mackey (Canada), E. Sanchez (Spain), A. Swierniak (Poland), P. Ubezio(Italy).

Organizing Committee: O. Arino, A. De Gaetano (Managing Director), A. Gandolfi, M. Kimmel.

Main topics covered in the courses and invited talks:

Cell Biology Basic biological mechanisms of the cell cycle and of cancerous transformation. Molecular mechanisms of cell cycle progression, oncogenes, cyclins, growth factors, checkpoints in the cell cycle, cell death and apoptosis, tumor growth and metastasis, angiogenesis and cytoskeleton.

Haemopoiesis Dynamics of haemopoiesis in normal and disease conditions: Structure of the human haemopoietic system, balance of production of precursors of blood cells, regulation feedbacks and their mathematical models, stability, oscillations and chaos in models of haemopoiesis, applications to explanation of causes of blood disorders.

Structured Cell Populations Methodology of construction and analysis of models of cell populations taking into account distribution of parameters of individual cells, in a deterministic and a stochastic framework: The age-size structure population density approach using partial differential equations, construction of the semigroup of operators for a linear model, nonlinear models and their qualitative behavior, examples of applications of deterministic models, models structured by discrete variables, overview of the expected branching process approach.

Cancer Therapy and Optimization Biochemical mechanisms and mathematical modeling of chemotherapy: types of cytotoxic drugs and their mode of action, cell cycle specificity, mechanisms of cell resistance, clinical protocols, mathematical models of cell cycle with control, basics of optimal control theory, optimization of chemotherapy protocols, Goldie and Coldman (clonal resistance) theory.

Cytometry and Parameter Estimation Methodology of measurements and analysis of joint distributions of parameters of cells in large cell populations. Principles of flow cytometry and related methods, use of flow cytometry to identify inner features of cells (chromosomes, organelles), mathematical models of cell population dynamics applied to interpreting flowcytometric data, flow cytometry as a diagnostic tools in cancer research. Basics of nonlinear model parameter estimation, geometry in parameter space, variance of estimates, sensitivity analysis, population estimates.

Stochastic Models in Cell Genetics Classical models of population genetics and modern methods based on coalescence, applied to studying variation in germ and somatic cells in culture and in organisms: the Fisher-Wright model of genetic drift with mutation, ancestral processes including the coalescent and genealogies of branching processes, principal models of mutations including the infinite alleles and infinite sites models and the stepwise mutation model, models of molecular evolution, dynamics of gene amplification and evolution of repeat-DNA, neutral evolution and tests of neutrality, mathematical models for diseases caused by dynamic mutations (expansions of triplet repeats), heterogeneity of populations of cancer cells.

Tentative list of instructors and invited lecturers: Zvia Agur, Ovide Arino, Jacques Belair, Edoardo Beretta, Alessandro Bertuzzi, Vincenzo Capasso, Ranajit Chakraborty, Mark Chaplain, Andrea De Gaetano, Alberto Gandolfi, Marek Kimmel, Michael Mackey, Joseph Mahaffy, Eva Sanchez, Andrzej Swierniak, Ziad Taib, Simon Tavare, Paolo Ubezio, Glenn Webb. Other speakers are being contacted.

29 June–3 July, 1999

First Announcement: Theory and Mathematics in Biology and Medicine 1999 Vrije Universiteit Amsterdam, The Netherlands June 29 - July 3, 1999

The international conference on Theory and Mathematics in Biology and Medicine 1999 aims to stimulate collaboration between mathematicians and bioscientists and to act as the main forum for the exchange of recent research results and new perspectives in the fields of Theoretical Biology and Medicine. This is the 4th of the official meetings, taking place every 3 years under auspices of the European Society for Mathematical and Theoretical Biology (ESMTB). In addition, it will be joint with the annual meeting of the Society for Mathematical Biology (SMB). The Netherlands Society for Theoretical Biology is responsible for the local organization. Through these links, this will be the first World Congress devoted to a rapidly growing, interdisciplinary domain of science where experimental biology and medicine, biochemistry, mathematics, computational science, physics and various fields of technology all come together.

Scientific Program The conference will cover the theory and mathematics from all disciplines within Biology and Medicine, including immunology, epidemiology, evolution, ecology, molecular biology, cell signalling, tumor growth and treatment, morphogenesis, pattern formation, metabolic modeling, protein folding, neuromodeling, computational biology, cardiovascular modeling, and biomechanics. In addition, special sessions will be organized around focused topics that are particularly new or rapidly gaining importance. Participants are strongly encouraged to forward suggestions regarding the scientific program to: tmbm99@bio.vu.nl

Further information For more information please visit the following web-site:

http://www.bio.vu.nl/tmbm99/ or contact the Conference Service of the Vrije Universiteit Amsterdam:

VU Conference Service Phone : +31-(0)20-4446790
De Boelelaan 1105  Fax :  +31-(0)20-4445825

    1081 HV Amsterdam Email : vu_conference@dienst.vu.nl

The Netherlands

Scientific Committee Zvia Agur, Wolfgang Alt, Albert Goldbeter, Lou Gross, Mats Gyllenberg, Reinhart Heinrich, Andreas Herz, Paulien Hogeweg, Yoh Iwasa, Vlastimil Krivan, Yuri Kuznetsov, Alan Perelson, Andrea Pugliese, Chris Sander, Angela Stevens

Organising Committee Andre de Roos, Frank van den Bosch, Paul Doucet, Odo Diekmann, Patsy Haccou, Hans Heesterbeek, Lia Hemerik, Jaap Kaandorp, Carolien de Kovel, Mirjam Kretzschmar, Bob Kooi, Matthijs Luger, Jaap van Pelt, Hans Westerhoff