The scientific report is written by Tom Britton after consultations with my co-investigators Fredrik Liljeros and Mia Deijfen.

The project has more or less followed the original application. Several research projects on dynamical processes on (social) networks have been finished and published by various combinations of the investigators and other co-authors. Below comes a short presentation of results according to the three sub-projects listed in the application.

a. Respondent driven sampling. Britton and Liljeros (together with a PhD student funded from other funds) have published a paper in Journal of Official statistics on the topic. The paper considers effects of the underlying network not being fully undirected, and what effect this has on estimators. A rule of thumb is shown saying that if this fraction exceeds 20%, then the estimators are misleading. A modification of the estimator is also proposed.

b. Heterogeneity in geographical networks. Here all three investigators have worked quite hard together trying to analyse a model in which individuals move around in space, and where both individuals and the underlying ground may be contagious. As an example of application it may be humans and doorhandles or similar, or cattle and their feces. This problem turned out to be harder than expected, and up until now no results leading to publications have been obtained.

c) “Partnership duration in heterosexual networks and their effect on the spread of STDs”. Britton and Liljeros have worked on this project together with another PhD student. The project was delayed due to sick-leave of the PhD student, but a manuscript is now ready for submission to the journal “Social networks”. The work concerns data from on sexual habits from a health clinic in Västra Götaland. The data consist of voluntary and anonymised information on number of partners and type and frequency of sex contacts during the last year. From the data we infer if individuals tend to have pre-defined strong will to use condoms or not, and if this will differ between men and women and between steady and casual partnership. A somewhat surprising and for health protection negative result is that individual use condoms less often in casual contacts (risky behavior) as compared to the first sexual contact with a partner-to-be.

During the third year of the project an international 4 days workshop gathering 20 researchers from various fields was organized in Sigtuna. The workshop was much appreciated by all participants, and several new research collaborations arose from the workshop. Another side effect of the workshop was that us three investigators are now part of an EU research project, Cost-Net, on network modelling and analyses. Thanks to this we, and in particular PhD students and post docs of ours, have participated in workshops and short courses. The list of participants of the workshop was as follows:

Mathisca de Gunst, Amsterdam, Mathematics
Mark Handcock, Los Angeles, Statistics
Fredrik Liljeros, Stockholm, Sociology
Mirjam Kretschmar, Utrecth, Medicine
Naoki Masuda, Bristol, Data science
Ernst Wit, Groningen, Mathematics
Petter Holme, South Corea, Physics
Tatyana Turova, Lund, Mathematical statistics
Tom Britton, Stockholm, Mathematical statistics
Vittorio Colizza, Paris, Physics
Robert Fitzner, Stockholm, Mathematical statistics
Rikard Sandell, Madrid, Sociology
Mia Deijfen, Stockholm, Mathematical statistics
Gianpaolo Scalia Tomba, Rome, Mathematics
Federica Giardina, Stockholm, Mathematical statistics
Pieter Trapman, Stockholm, Mathematical statistics
Svante Janson, Uppsala, Mathematics
Kristoffer Spricer, Stockholm, Mathematical statistics
Disa Hansson, Stockholm, Mathematical statistics
Luis Rocha, Stockholm, Criminology

In the reference list we give a complete list of all publications by us in the area of research project. In most publications Riksbankens jubileumsfond is explicitly acknowledges, and nearly all publications are  open access. The investigators have also presented results at various international conferences.

Several PhD students have been involved (but not financed) in different publications, thus also educating new people into academia.

The grant has been used mainly for salaries for Deijfen, Liljeros and Britton, for the above mentioned workshop, and to a lesser extent for conference trips and open access publications. During the project period, Deijfen has been promoted to full professor.