Modelling of the spatio-temporal distribution of rat sightings in an urban environment

The brown rat lives with man in a wide variety of environmental contexts and adversely affects public health by transmission of diseases, bites, and allergies. Understanding behavioural aspects of pest species can contribute to their effective management and control. We report an analysis of the spatio-temporal distribution of rat sightings, which are directly related to rat infestation, in a district of Madrid (Spain). We first consider an empirical analysis of the first-order for the first and second order properties of the spatio-temporal point process of rat sightings, in which we model the first-order intensity function as a product of two intensity functions, one spatial and the other temporal, and use the inhomogeneous spatio-temporal KK-function to estimate second order properties. We then formulate a more mechanistic model in which the conditional intensity of the point process depends explicitly on its past history. We have found that the sightings show strong seasonal variation and are strongly influenced by environmental factors related to human behaviour. We have also identified spatio-temporal clustering and interaction over and above the separate temporal and spatial components of variation in risk, and have estimated the spatial scale on which the interaction operates.