Random graph models predict the spread of infection

Svante Janson has dedicated his life to mathematics. At the age of 12 he was granted special permission to attend university. Today he is a world authority. The mathematical models he studies can be used, among other things, to predict the spread of infectious diseases, but can also be applied on democracy.

Svante Janson

Professor of Mathematics

Wallenberg Scholar 2011
Grants 5 + 5 years

Institution:
Uppsala University

Research field:
Mathematical analysis, probability theory, combinatorial probability, in particular random graphs, and also analysis of algorithms.

The Swedish general election in 2010 drew attention to problems with the proportional election system, in which some parties benefited from the fact that there were not enough “top-up” (or “adjustment”) seats to fully mirror the votes cast by the electorate. Svante was involved in the review of the system.

“Among other things, I have met the members of the Electoral Reform Commission to present mathematical calculations. I don’t usually accept work of this kind, but I find this project enjoyable. It is a fairly simple problem in purely mathematical terms, but still involves an element of challenge,” Svante says.

He does not need any expensive equipment for his research. His office at the Ångström Laboratory in Uppsala is piled high with papers and periodicals, just as one would expect of a mathematics professor. Svante himself has written four books and over 250 scientific articles.

“I prefer working on paper instead of the computer,” he says with a smile.

“I feel doubly honored to receive recognition in this way – first by the university, which nominated me, and then, by being selected in the face of tough competition. Things are an awful lot easier with funding of this kind. Now I have to make best use of the money.”

Random graphs shed light on epidemics

Random graphs are one of Svante’s central areas of research. Uses of graphs include describing networks in various applications. One example is the internet, either as a physical network of computers or as a logical network of websites and links. But also included are social networks, food chains or paths for the spread of infection in a population.

A graph consists of a given number of nodes (also called vertices), and a number of edges, which link two nodes. In a random graph either the nodes or the edges are added randomly. Svante is studying and developing the theoretical model; other researchers will then be able to use the model in a realistic context.

“A topical example of such an application lies within the field of epidemiology, where a graph is conceived on which the nodes are inhabitants of Sweden, for example, and the edges represent all instances of contact between two people by which one can infect the other with a certain disease, such as influenza,” he explains.

The model cannot precisely describe the entire population of Sweden, and how people have contact with each other.

“But data can be obtained on average conditions, and it may be assumed that they are random within given parameters. If the model is good, it may also say something about reality. Other experts can therefore use various random graph models to try to predict the spread of infection and the effect of vaccinations.”

Sorting large quantities of data

“The same type of mathematical problem recurs in other contexts, e.g. in data science applications. This may involve mathematical methods of sorting large quantities of data – thousands or millions of items – for further processing. This requires continuous refinement of the mathematics,” Svante points out.

“Data scientists have long used a number of mathematical methods, but since computers are so much faster nowadays, much larger problems are tackled, which demand even better methods. The old methods work, but may no longer be the best. This results in a constant stream of new problems including mathematical ones.”

Researchers in mathematics are often described as lone wolves, and it is true that they do much of the work on their own. Being appointed a Wallenberg Scholar increases the ability to travel and meet foreign colleagues.

“I have worked with a number of researchers at Cambridge in England. Overall, the university there is the foremost European center of excellence in the mathematical sciences. Hitherto I have only been able to stay for a month at a time at most, but now I hope to be able to spend entire semesters there. I will also be able to afford to organize conferences and invite researchers here to Uppsala.”

Notwithstanding the solo nature of the work, personal meetings are very important in mathematical research.

“Much of the detailed work can be done alone, but it is best if fundamental ideas are discussed at personal meetings. A large part of my research comprises small projects resulting from personal meetings at conferences. I usually say that the most important things are the intervals between lectures, when one has the opportunity to talk to people.”

Started university at the age of 12

Svante can be described as something of a prodigy. At the age of nine he passed the high school chemistry exams, left elementary school and began attending lessons at the high school in his home town of Borlänge, central Sweden.

“The local board of education exempted me from the requirement to attend elementary school, and when I was 12 I was granted special permission to enroll at university.”

Since then math has been his life. He obtained his B.Sc. at the age of 14, and has PhDs in both mathematics and mathematical statistics.

He is fascinated by the major fundamental questions.

“I mostly study random problems without any direct link to applications. I study problems for their own sake,” Svante explains.

Text Nils Johan Tjärnlund
Translation Maxwell Arding
Photo Magnus Bergström