Critical epidemics, random graphs, and Brownian motion with a parabolic drift
Critical epidemics, random graphs, and Brownian motion with a parabolic drift
We investigate the final size distribution of the SIR (susceptible-infected-recovered) epidemic model in the critical regime. Using the integral representation of Martin-Löf (1998) for the hitting time of a Brownian motion with parabolic drift, we derive asymptotic expressions for the final size distribution that capture the effect of the initial …