The basic-reproduction number of infectious diseases in spatially structured host populations

The spatial structure of a host population has a profound effect on the dynamics of infectious diseases. The basic reproduction number, a central quantity in the study of epidemic dynamics, is affected by host clustering as well as host density.

Several authors have developed methods to quantify the basic reproduction number in a spatially structured host population. The methods used and the expressions derived are however difficult to apply to real life spatial host structures. In this paper we introduce an explicit expression for the basic reproduction number using the O-ring statistic, developed in spatial statistics, that quantifies the host density as a function of the distance from a randomly selected host individual. The O-ring statistic is frequently used in the study of the ecology of spatially structured plant populations, being a convenient summary of the properties of a landscape by way of a single function.

The connection we develop between spatial statistics and epidemic dynamics can be used to study the effect of host spatial pattern on the basic reproduction number of infectious diseases. As well as showing how explicit expressions for the basic reproduction number can be derived for landscapes with standard structures, our expression for the basic reproduction number is tested against a simulation model. The model structure in our simulation is motivated by the spread of a plant disease epidemic, although it is applicable more broadly. The agreement between our analytic expression for the basic reproduction number and the corresponding numeric quantity extracted from simulations is close to perfect across a wide range of landscape structures and model parameterisations, and including cases in which more than one species is at risk of infection.