Title: Survival dynamics for the contact process with avoidance on $Z, Z_n$, and the star graph
Speaker: Matthew Wascher (Ohio State University, Statistics)
Abstract: We consider the contact process with avoidance, a modified contact process, on directed graphs in which each healthy vertex can avoid each of its infected neighbors at rate $\alpha$ by turning off the directed edge from that infected neighbor to itself until the infected neighbor recovers. This model presents a challenge because, unlike the classical contact process ($\alpha = 0$,) it has not been shown to be an attractive particle system. We study the survival dynamics of this model on the lattice $Z$, the cycle $Z_n$, and the star graph. On $Z$, we show there is a phase transition in $\lambda$ between almost sure extinction and positive probability of survival. On $Z_n$, we show that as the number of vertices $n \rightarrow \infty$, there is a phase transition between log and exponential survival time in the size of the graph. On the star graph, we show that as $n\rightarrow \infty$ the survival time is polynomial in $n$ for all values of $\lambda$ and $\alpha$. This contrasts with the classical contact process where the the survival time on the star graph is exponential in $n$ for all values of $\lambda$.
