## Center for Applied Mathematics Colloquium

Abstract:

Spreading processes, as in infectious diseases, social behaviors, or computer viruses, impact biological, social, and technological systems. To manage spreading in a systematic way, models are needed that predict spreading dynamics in terms of a few parameters. We study a spreading model in which interacting agents can adapt susceptibility to a spreading process after first exposure. The model is motivated by an investigation of foraging behavior by desert harvester ants. Using an analytically tractable model that predicts behaviors exhibited in field data, we showed how resilience of colony foraging rates to changing temperature and humidity can be explained by ants modifying their susceptibility to the spread of foraging, once exposed to outside conditions.

To generalize these results, we propose and analyze a network model with adaptive susceptibility and agent heterogeneity. We show how four dynamic regimes are distinguished by four numbers that depend on network structure and heterogeneity. We prove features of the geometry of solutions that dictate both transient and steady-state possibilities. For example, in the bistable regime, not captured in traditional models, there can be a rapid cascade after a long period of quiescence. We use our analytical results to design control strategies that suppress or promote spreading.

This is joint work with Renato Pagliara and (for the ant foraging study) Deborah Gordon.

Bio:

Naomi Ehrich Leonard is Edwin S. Wilsey Professor of Mechanical and Aerospace Engineering and associated faculty in Applied and Computational Mathematics at Princeton University. She is a MacArthur Fellow, and Fellow of the American Academy of Arts and Sciences, SIAM, IEEE, IFAC, and ASME. She received her BSE in Mechanical Engineering from Princeton University and her PhD in Electrical Engineering from the University of Maryland. Her research is in control and dynamics with application to multi-agent systems, mobile robotic sensor networks, collective animal behavior, and human decision dynamics.