# Des Higham and Henry-Louis de Kergorlay have derived new results about the spread of disease in an article published in the Proceedings of the Royal Society: Series A

Des Higham and Henry-Louis de Kergorlay in the University of Edinburgh, School of Mathematics, have derived new results about the spread of disease in an article recently published in the Proceedings of the Royal Society: Series A

Epidemics on hypergraphs: spectral thresholds for extinction

Traditional network-based models use information about pairwise contacts --- if A and B work in the same office then the disease may pass between them. However, real human interactions are not simply based on pairwise encounters. We typically come together in groups; for example in households, workplaces and classrooms, or through social encounters. New mathematical models are needed in order to take account of such group structures. For example, if there is a viral load effect, then sharing a car with three passengers may be more than three times as risky as sharing a car with one passenger. By contrast, if a photocopier is regularly cleaned, then sharing it with three colleagues may be less than three times as risky as sharing it with one colleague. Such considerations lead to what mathematicians may describe as nonlinear infection rates on hyperedges.

The focus of this new work is to find conditions under which a disease is guaranteed to die out, generalizing the widely quoted notion of "Rzero". The resulting mathematical expressions neatly separate the influence of (a) underlying virulence of the disease, (b) the group connectivity structure across the population, and (c) individual responses, such as social distancing and mask-wearing. Hence, we gain insights into the effect of governmental and public health interventions.

Following on from this initial theoretical study, the authors plan to apply these ideas to realistic "what-if" computer simulations at a city level.