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