Hazards, spatial transmission and timing of outbreaks in epidemic metapopulations

Highly infectious, immunizing pathogens can cause violent local outbreaks that are followed by the agent's extinction as it runs out of susceptible hosts. For these pathogens, regional persistence can only be secured through spatial transmission and geographically asynchronous epidemics. In this paper we develop a hazard model for the waiting time between epidemics. We use the model, first, to discuss the predictability in timing of epidemics, and, second, to estimate the strength of spatial transmission. Based on the hazard model, we conclude that highly epidemic pathogens can at times be predictable in the sense that the waiting-time distribution between outbreaks is probabilistically bounded; The greater the spatial transmission the more periodic the outbreak dynamics. When we analyze the historical records of measles outbreaks in England and Wales between 1944 and 1965, we find the waiting-time between epidemics to depend inversely on community size. This is because large communities are much more tightly coupled to the regional metapopulation. The model further help identify the most important areas for spatial transmission. We conclude that the data on absence of these pathogens is the key to understanding spatial spread.