By Hans Kaper
As discussed in last week’s recap, participants of the summer school on “Dynamics and Data in the COVID-19 Pandemic”—organized by the American Institute of Mathematics (AIM) and the Mathematics and Climate Research Network (MCRN)—had previously identified 15 research questions, which were organized under five “umbrellas:”
- Diseases and the Environment
- Impacts of Human Behavior
- Incorporation of Data
- Resource Allocation
- Social Justice.
Students spent most of the online program’s fifth week in small groups to drill down on the questions, develop mathematical models to address the questions, elucidate the models’ underlying assumptions, identify relevant data to test the models, and relate the models’ output to the original queries. Two “all-hands” meetings—at 11 a.m. and 5 p.m.—framed the daily schedule.
At the afternoon all-hands meetings, the five umbrella groups presented brief summaries of their progress.
On Tuesday morning, Henri Berestycki (École des hautes études en sciences sociales) gave a lecture on “Spatial Modeling of COVID-19” that described numerous mathematical models, including nonlocal contamination, which lead to the summer school’s first theorem: Pandemic Threshold Theorem. Other topics addressed the pandemic spread in a periodic medium, traveling waves, susceptible-infectious-recovered (SIR) models with diffusion, and a recent case study by Marino Gatto and his collaborators (published in PNAS) in Italy about expressways’ effect on disease spread. The authors of the latter work used an augmented SIR model (SIRT) to analyze an epidemic’s spread in a half-space; the “T” in SIRT represents travel by infected individuals on the boundary.
The lunch period was dedicated to tutorials on data assimilation and bifurcation theory, a discussion on applying for the NSF’s Graduate Research Fellowships Program, and a conversation on stereotype threats. Tai-chi sessions at the start of each afternoon’s assembly prevented an outbreak of Zoom fatigue.
With only one more week to go, everyone is looking forward to the group reports, which are promised on Thursday, July 30.
Hans Kaper, founding chair of the SIAM Activity Group on Mathematics of Planet Earth and editor-in-chief of SIAM News, is affiliate faculty in the Department of Mathematics and Statistics at Georgetown University.