Reducing disease spread through optimization: limiting mixture of the population is more important than limiting group sizes

One of the most ecient tools for limiting the disease spread during a pandemic is to limit the contacts between people. However, too strict restrictions may seriously aect the economy, health, education, and well-being of people. Hence, in this paper we study the use of individualized strategies instead of uniform restrictions for the organisation of activities that include close contacts. Concretely, we study how to schedule a set of activities where the participants meet, and hence can spread infection. Those could be classroom teaching, sports activities, work shifts, etc. Formulating the contacts resulting from the assignment of participants to scheduled activities as a graph, we propose to search for graph structures that limit the disease spread. We develop a mathematical algorithm for identifying such favorable graphs by limiting the distinct contacts the individuals meet during an activity. The quality of a contact graph is evaluated using an agent-based model where individual disease progress is dened according to the so-called SEIR (Susceptible, Exposed, Infectious or Removed) model. A computational study targeted towards the re-opening of physical lecturing at a major university, using real-life data from a course database, demonstrates the ability of this algorithm to limit the spread of a disease under several realistic setups, and shows that the infection can be signicantly reduced while also limiting the part of population in quarantine when using this algorithm versus just a general group size limitation. Specically, it shows that individualized re-opening strategies that limit the mixing of populations can be more powerful in reducing disease spread than limiting group size.