Friday, April 1, 3:00 p.m.
Center for Social Complexity
3rd Floor Research Hall

Evelyn Sander, Associate Professor
Dynamical Systems and Differential Equations
Department of Mathematical Sciences
George Mason University

Epidemics in the presence of social attraction and repulsion

ABSTRACT: We develop a spatiotemporal epidemic model incorporating attractive-repulsive social interactions similar to those of swarming biological organisms. The swarming elements of the model describe the ability of distinct classes of individuals to sense each other over nite distances and react accordingly. Our model builds on the non-spatial SZR model of [Munz, Hudea, Smith?, 2009] modeling a specific epidemic, namely the attack of zombies. This case is interesting from the modeling standpoint, as zombie epidemics are particularly virile, albeit restricted to a theater near you and certain parts of San Francisco, Washington D.C., and other major metropolitan areas []. Spatial effects not only enhance entertainment value (as a cinematic portrayal of a spatially invariant zombie attack would be somewhat lacking in thrill) but are critical to understanding the epidemic. We show that in the absence of a cure for zombiism, the alert human population will eventually be annihilated, but at a slower rate than in the non-spatial model. The extra time to extinction might allow the development of a cure. We also show that without any assumption of collusion, the system self-organizes into transient traveling pulse solutions consisting of a swarm of zombies in pursuit of a swarm of alert humans. In the presence of a zombie cure, the traveling solutions exist persistently and stably for all time.