Space-Time Interactions in Multiregion Disease Modelling

Abstract

In this paper, some methods for representing space and time consistently within a deterministic version of the recurrent epidemic model are examined. First, a general framework for transforming a model for a single community into a multiregion counterpart where the frequency of contact between susceptibles and infectives is some inverse function of distance is described. Different spatial interaction representations of the accessibility of the regional populations to one another are shown to induce variations in the temporal behaviour of the disease model which are conditional on whether the specification allows for a single infectivity rate or a set of regionally variable rates. The second of these specifications is shown to induce lead and lag times between the simulated regional disease-incidence and the average study-area cycle. In the central section of this paper, the relationship between these temporal effects and the accessibility of the region which is the source of the simulated epidemic is analysed. Last, the assumption of a static equilibrium is relaxed to allow for the combined effects of population distribution and regional accessibility on the consistency of the alternative specifications to be assessed.