The last day of the week was devoted to several exercises and some self-reflection. Anonymous polling was part of each exercise.

*First exercise*: Think about questions that you would like us to address, given what we have heard during the week and keeping in mind that ultimately these questions have to be translated into the language of mathematics. Many suggestions came up, too many to be listed here. Among the top candidates were surveillance testing, analyzing the spread of epidemics among selected subgroups of a population, optimization of test locations, optimization of methods for group testing, socio-economic stratification, applying epidemiological methods to the spread of misinformation, and dynamics of concurrent diseases.

*Second exercise*: Give your view of the role of mathematics in the study of the COVID-19 epidemic. The top-rated answer to this question was a surprise: “I am not sure.” Once this answer came up, it quickly gained traction. Clearly, many of us shared this feeling of uncertainty but were hesitant to express it. Other answers were more aspirational; the second-rated was “Informing public policy.”

*Third exercise* (after a Tai-Chi session): What does the word “model” mean to you? While the term is used in many disciplines, it can have very different meanings. Take-home lesson: it is important to figure out what is meant in a given context.

The afternoon ended with a vigorous game of Ultimate Tic-Tac-Toe, a novel challenge for almost all participants.

Homework for the weekend:

Read “*The Mathematics of Infectious Diseases*” by Herbert W. Hethcote, , SIAM Review (2000), 42(4), pp. 599-653, through Section 2.5.

What Did We Learn during Week 1?

We got a general introduction to the topic of the summer school: the dynamics of epidemics, data, and COVID-19. We got an overview of the problems, we heard from experts, and got a taste of the available data and models. Not much mathematics, and not much depth, but a good preparation for the real work that is yet to come. We also got to know each other, learned how to navigate the virtual conference center, and we explored options for future projects.

Looking forward to Week 2, when we will discuss epidemiological models in more detail.