Extinction Times and Phase Transitions for Spatially Structured Closed Epidemics

摘要

This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous Rigorous results can be heuristically explained in terms of the more transparent Dynamics of an approximating deterministic system. The model is then extended To include a host population structured into patches, with weak nearest-neighbour Mixing of infection. It is shown, by considering the approximating deterministic System, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N ＞ N_c where N_c is a Critical patch size below which transits are unlikely to occur.