Young Researchers Workshop:
Kinetic and macroscopic models for complex systems

Contagion shocks in one dimension

Li Wang

University of California, Los Angeles

Contagion models involve emotional states that affect individuals? behavior. We consider an agent-based contagion motion model in one dimension that has recently been studied in the artificial intelligence community. The model involves movement proportional to a "fear" variable which undergoes a temporal consensus averaging based on distance to other agents. We consider "Riemann initial data" for this problem corresponding to shock dynamics in a continuum limit. We consider distinguished limits as the contagion interaction distance and the interaction timescale vanishes. The limiting behavior is related to a classical model for pressureless gas dynamics with "sticky" particles. In comparison we observe a threshold for the interaction distance vs. interaction timescale that produce qualitatively different behavior for the system - in one case particle paths do not cross and there is a natural Eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model in the continuum limit.