This thesis is based on Bayesian hierarchical spatial models for the study of diseases in agricultural groves. This methodology have been little used in agricultural Epidemiology . The need to control the spatial variability present in 
most of the observed data in agriculture, requires finding new ways of modeling capable to properly collect the structure 
of relationships between individuals studied. In this sense, the overall aim of the thesis is the contribution of general modeling tools in the field of spatial analysis for the study of the presence of a disease in agricultural groves and 
that help to describe the distribution patterns of infection when we have few data and in absence of explanatory variables.

In Chapters 2 and 3 we proposed hierarchical models capable to study data associated a lattice of fixed locations and in 
they are considered a temporal component through a covariate that collects the history of the disease over time. In particular, in Chapter 2, are constructed dynamic models with spatial structure and they are considered unobserved 
sources of variability (effect of heterogenity) on the other hand, in Chapter 3 we present three modeling in the context of survival data. In each of them, we estimate survival time of individuals affected by the evolution of a disease over time and by the presence of unobserved heterogeneity. Thanks to the time-dependent covariate considered in the three modelings and to building a dynamic spatial structure (frailty) is possible relax the restriction of the proportional hazards Cox model. 
These proposals framed in the context of spatial-temporal models.

In Chapter 2, we show that the dynamic of risk is determined by information that depends of past (process history ) and 
by a random effect of present. In these effects be reflect unobserved variability (heterogeneity) and spatial variability. Likewise, in the Chapter 3, we show that starting from observed data in a lattice of fixed locations is possible build  survival models. Thanks to the three models developed in this chapter, we can think of modeling the hazard function from three different perspectives. We start with a Weibull model with discretized times over periods of one year and we continue with two proposals based on counting processes. These latter two modeling are distinct because on one hand is considered a Gamma process in the prior distribution that defined to the baseline hazard function and in the second is assigned a polygonal function to this baseline hazard.

In Chapter 4, we propose a hierarchical model capable to predict at any point in the region, the probability or risk of disease by one individual in the agricultural context. Thank the methodology SPDE-INLA, it is possible to propose a Structured Additive Regression model with spatial effect (known as Latent Gaussian model) with random variable Bernoulli controlled by a few hyperparameters.

With the methodology developed in Chapter 4 it is possible to predict (kriging Bayesian) the occurrence of a phenomenon 
in a continuous region. Using the kriging Bayesian we can incorporate sources of uncertainty associated with the prediction parameters which leads to more realistic and accurate estimates. It is also possible to build risk maps through which we 
can estimate the uncertainty both in places observed as well as unobserved. The INLA methodology combined with the SPDE approach provides an excellent theoretical framework for predicting phenomena. The illustration of the methodology with 
real data allows recognize its usefulness in epidemiological studies not only in the agricultural context.

In general the various proposals of modeling recognize the existence of a small-scale spatial correlation. The illustration the methodology with real data allows recognize the importance of spatial variability and it is thanks to her that we may come to understand the dynamics of a disease and the mobility pattern of disease causing agents in groves agricultural. 
The models with best fit have in their structure the effect of the covariate with the history of the disease and the influence of a dynamic spatial random effect.

Tackle problems from the epidemiological context requires us to understand the process statistically. Therefore, we need 
to design models capable of capturing unobserved heterogeneity that is not usually explained in the available covariates.  
To think that individuals are drawn from a homogeneous population is inadequate, especially in phenomena where there are hidden risk factors that are shared due to the proximity between subjects. Thus, design hierarchical models that allow us 
to represent the heterogeneity of the population in any of their layers or levels seems appropriate. Therefore study a spatial process using  the hierarchical models from the Bayesian paradigm allows build useful tools in epidemiological studies in any context.  Also allow us to study the incidence and the distribution of a phenomena associated with a 
spatial process. In particular, usefulness of methodology proposal is demonstrated in agriculture context.