Explore the intersection of mathematics and epidemiology in this inaugural lecture by renowned mathematician Henri Berestycki. Delve into the application of reaction-diffusion systems to model the spread of epidemics, with a focus on the COVID-19 pandemic. Learn about the various forms of diffusion in epidemiological models and their implications for disease spread. Discover recent research on spatial spreading of COVID-19 in France using graph-based diffusion models, the effects of fast diffusion along transportation networks, and the impact of individual behaviors and social diffusion on epidemic dynamics. Gain insights from Berestycki's extensive experience in nonlinear partial differential equations and their applications to biology, ecology, and social sciences.