This mini-course serves as an introduction to the mathematical theory of the SI and Bass models on networks. The SI model describes the spreading of epidemics; the Bass model describes the spreading (diffusion) on innovations. The focus in this course will be on understanding how the network structure affects the spreading process. The first part of the analysis will be exact (no mean-field type approximation. A second part will deal with the dynamics of diffusion of innovation over time-varying networks and will rely on mean-field approximations and simulation results.

Guest Lecture: Gadi Fibich is a Professor of Applied Mathematics at Tel Aviv University, Israel. He received the B.Sc. degree (Summa Cum Laude) and the M.Sc. degree in Applied Mathematics from the Technion, Israel, and the Ph.D. degree from the Courant Institute at New York University, USA. His academic career includes positions at UCLA and Tel Aviv University, where he has served as a lecturer, senior lecturer, and associate professor before becoming a full professor in 2007. Between 2014 and 2016, he was a Visiting Professor with the University of Maryland, USA. From 2017 to 2021, he chaired the School of Mathematical Sciences at Tel Aviv University. His research interests span mathematical modeling, the spread of innovations and epidemics on networks, nonlinear optics, nonlinear pricing, and auction theory. -------------------------------------------------------------------------------------------------- Tentative plan: 1. The compartmental SI and Bass models. The Bass and SI models on networks 2. Derivation of master equations on networks and hypernetworks 3. Complete and circular networks, explicit calculation of the infinite-population limits 4. The indifference principle and the dominance principle. Applications 5. Universal lower and upper bounds 6. Diffusion of innovation over time-varying networks (activity-driven)

On site

Oral presentation

P.D.2-2 - March

Course schedule: • Tuesday March 11, 2025 – 15:00-18:00 – Clarke Room (DET, Cittadella, 1st floor) – Prof. Fibich • Thursday March 13, 2025 – 15:00-18:00 – Clarke Room (DET, Cittadella, 1st floor) – Prof. Fibich • Monday March 17, 2025 – 15:00-18:00 – Clarke Room (DET, Cittadella, 1st floor) – Prof. Fibich • Tuesday March 18, 2025 – 15:00-18:00 – Clarke Room (DET, Cittadella, 1st floor) – Prof. Fibich • Wednesday March 19, 2025 – 12:00-15:00 – Clarke Room (DET, Cittadella, 1st floor) – Prof. Rizzo