Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with demographic noise, including the susceptible-infected-recovered (SIR) model and its general extensions. In the limit of large, well-mixed populations, we compute the probability distribution for all extensive outbreaks, including those that entail unusually large or small (extreme) proportions of the population infected. Our approach reveals that, unlike other well-known examples of rare events occurring in discrete-state stochastic systems, the statistics of extreme outbreaks emanate from a full continuum of Hamiltonian paths, each satisfying unique boundary conditions with a conserved probability flux.
We further show that the interplay between demographic noise and network heterogeneity can have a non-trivial effect on the final outbreak size and its distribution.
Finally, we discuss the role of time-varying rates (i.e., lockdowns) and how these influence the epidemic’s outcome.
Prof. Flavio Seno
