Orateur
Description
The Zombie Infection Model (ZIM) is a variant of the stochastic SIR model on graphs in which infected nodes are not removed spontaneously, but are instead killed by their susceptible neighbours: a susceptible node becomes infected at rate λ times its number of infected neighbours, while an infected node is removed at rate 1 times its number of susceptible neighbours. This places the ZIM within the class of interacting particle systems, as a hybrid of the SIR and biased-voter (Williams–Bjerknes) models, and produces rich and sometimes counterintuitive behaviour. I will present a first rigorous analysis, focusing on the survival probability — the chance the infection spreads indefinitely — and its monotonicity. On trees this probability is monotone in λ, yet there exist bounded-degree graphs on which it is not. Via couplings with random walks and percolation, we further obtain extinction criteria and survival bounds on complete graphs, regular trees, and Z^d.