The math behind social distancing: the rules that influence epidemic behavior

Tokyo, Japan – Studying epidemics can help us plan for the future and identify better ways of dealing with them. Now, in a new study published in Proceedings of the National Academy of Sciences, a multi-institutional research team led by the Institute of Industrial Science, The University of Tokyo, has worked out how to understand social-distancing behavior. 

The research team obtained a solution for a complex optimization problem that describes how individuals adapt their behavior during an epidemic in order to balance the costs of infection and social distancing. A central assumption is that people are behaving rationally—they are seeking to obtain the best outcomes for themselves.

Through their work, the team identified simple rules, previously unrecognized, that govern this decision-making. The team’s mathematical models demonstrated that the social distancing of rational individuals ought to be proportional to the number of cases and the infection cost.

“What we found was surprisingly simple,” says Simon Schnyder, lead author of the study. “Although this behavior was previously thought to be quite complex, our results support the intuition that with greater infection cost and more cases, more rational social distancing will occur.”

The team provides clear guidelines for predicting population behavior based on just two factors: the disease’s basic reproduction number and the estimated cost of infection. Using these, officials can forecast whether a population will engage in significant voluntary social distancing or continue normal activities. This would explain why during the COVID-19 epidemic we saw a reduction in socializing, even in societies in which no public lockdowns were enforced.

“Our findings may seem straightforward, but being able to offer a simple mathematical explanation for this complex behavior represents a major advance in the field of behavioral epidemiology,” explains Matthew Turner, senior author of the study. This work also gives scientific validation to public health approaches that were developed intuitively during previous epidemics like HIV.

The results of this study will be useful for governments who need to design intervention strategies for future epidemics. Furthermore, the study offers a useful target for members of society to aim for when the next epidemic comes around: act rationally.

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The article, “Understanding Nash Epidemics,” was published in Proceedings of the National Academy of Sciences at DOI: 10.1073/pnas.2409362122.

About Institute of Industrial Science, The University of Tokyo

The Institute of Industrial Science, The University of Tokyo (UTokyo-IIS) is one of the largest university-attached research institutes in Japan. UTokyo-IIS is comprised of over 120 research laboratories—each headed by a faculty member—and has over 1,200 members (approximately 400 staff and 800 students) actively engaged in education and research. Its activities cover almost all areas of engineering. Since its foundation in 1949, UTokyo-IIS has worked to bridge the huge gaps that exist between academic disciplines and real-world applications.