Spatial statistic modelling of rat sightings

Resumen

In the last few decades, changes in cities have facilitated the proliferation of pests and corresponding diseases associated with them. Cities have expanded through natural habitats of rodents and other pests, resulting in the reactivation of diseases that were thought to be extinct. Urban plagues are often the cause of important expenses of public administrations in tasks and strategies trying to eradicate them. One of the most harmful plagues comes through the Rattus norvegicus, prevalent species in the majority of European cities. The brown rat (Rattus norvegicus ) lives with mankind in a wide variety of environmental contexts and adversely affects public health by transmission of many diseases to humans and animals, such as Salmonellosis (Salmonella enterocolitis), Murine typhus (transmitted by the rat flea), Weils disease (spread by rat urine), Hantavirus, Leptospirosis, Cryptosporidium parvum, Hemorrhagic viral fever and Q fever (Quy et al., 1999). Understanding behavioural and spatial correlation aspects of pest species can contribute to their effective management and control. The purpose of this thesis is to determine the spatial structure of rat sightings, considering two alternative ways relative to the data set: -Rat sightings can be considered non-trivial observations that are taken at a finite number of sites constituting the entire study region. -Rat sightings can be described by spatial coordinates in a particular region of interest defining a spatial point pattern. The first approach, which is widely detailed in Chapter 2, will be treated and processed as lattice data. Unlike geostatistics, there is no possibility of a response "between" data locations. Data locations are regions. Examples of lattice data are: - Presence or absence of a plant species in square quadrants over a study area. - Number of deaths due to a severe disease. - Pixel values from remote sensing (satellites airborne). The second approach will be developed in Chapter 3 and Chapter 4. At present, there are only few references on the modelling of the spatial and the spatio-temporal distribution of urban pests, particularly if we consider a methodological approach for modelling continuous point-generating processes leading to spatial point patterns. The literature keeps on being scarce if we extend and complete such an approach with an application of spatial copulas to model the spatial dependence of rat sightings in an urban area, using complex components such as distances to an attractor point in an urban environment (markets, feeding stations for cats, water sources and green areas). In Chapter 1, we present a brief theoretical framework of lattice data models and present two approaches to model spatial point patterns through copulas as a mathematical tool for dealing with the concepts shown along the next chapters of this thesis. In Chapter 2, we investigate the spatial distribution of rats in a traditional district of Madrid, Latina, using distances from each of a number of focuses as indirect measures to favourable situations which allow the proliferation of rats. We extended the standard Poisson regression model by the inclusion of a multiplicative non-linear function and an unstructured random effect and a spatial random effect to account for the spatial structures of the data. The function's shape combines an elevated risk of presence close to the source with a neutral effect at large distances. We also included socio-demographic covariates in the model to control potential confounding. In Chapter 3, we study the spatial structure of rat sightings and its relation to a number of distance-based covariates that relate to the proliferation of rats. Given a number of locations biologically considered as attractors points (Ayyad et al., 2016a), spatial dependence will be modelled by distance-based covariates and angular orientation, both relative to those particular points. We use copula functions to build a particular spatial multivariate distribution using univariate margins coming from the covariate information, and we finally model the spatial dependence and spatial prediction of distances and angular orientation. We use maximum likelihood together with the Bee algorithm to estimate the corresponding parameters, and perform prediction of rat sightings according to the predefined six focuses in Latina district (Madrid city). The purpose of this chapter is to determine the spatial structure of rat sightings in relation to some established attractor points and spatially related covariates based on distances to water sources, green zones, markets and cats feeding, and angular orientation. In particular, we aim at finding a probabilistic model via non-Gaussian copulas that is able to reproduce the proximity to a potential attractor focus, given the angular orientation and Euclidean distance. In Chapter 4, we model the spatial dependence and spatial prediction of counts of rat sightings in Madrid city with the help of vine copulas. Distance-based covariates that relate to the proliferation of rats and neighbourhood counts enable the spatial structure of rat sightings. We use copula functions to build a particular spatial multivariate distribution with a mixture of univariate margins. In order to deal with the discrete zero-inflated counts and covariate neighbourhood count, we present an approach that allows to assign conditional random ranks to the discrete data. This way, we mimic a continuous variable easing the vine copula estimation. This thesis is mainly focused on developing spatial models for rat sightings, i.e. to model spatial urban rat behaviour analysing two different approaches. The first approach considers rat sightings as lattice data and the second approach considers the sightings as point patterns. Motivated by the aim to model the rat sightings spatial dependence structure that we propose in the two different approaches, we use non-linear regression for the first case and copulas for the second case. Every chapter adds some valuable information over the previous ones. Finally, we present a general summary of the currently ongoing research projects which have emerged motivated by the necessary extension to space-time rat sightings modelling and, as a consequence, we come to the conclusion that the models proposed in this thesis can be improved by introducing a temporal component, characterised by the week of the month in which there has been sightings of rats.