Modelagem de processos estocásticos espaço-temporais e de percolação no estudo de risco sobre sistemas : uma aplicação ao estudo da transmissão à febre aftosa

Abstract

The foot and mouth disease (FMD) is a disease that attacks all cloven-hoofed animals, especially cattle, pigs, sheep and goats. It is characterized by blistering and considered the most serious of all infections. It is generated by at least seven serotypes of viruses that cause infections indistinguishable. The spread is associated with the movement of infected animals and their contact with susceptible animals. In this thesis a model was proposed which aimed to find an index of risk of transmission of foot and mouth disease virus between cattle farms across a network. It comprises two levels, the first will be analyzed the point process F generated from the xi ∈ A ⊂ R2 randomly selected points and the stochastic process Yxi,tj , the level of infection wich through it is done the location of the occurrence of infection by the FMD virus, called a focus of infection. The second level is a percolation model G(G, P), in wich G = G(F,E) is a graph, F a set of farms and E represents the edges that connect the farms. And P is the probability that transmission occurring. By uniting the two levels arises G′(G′, P′), in that G′ consists of F′ the union of all the farms to the set F focus F, and E′ the union of E edges with new edges connecting F and F. And P′ is formed by the set of values of P and Pi,l, the probability of farm Fi be infected by a foco fl. Points were simulated representing the cartesian coordinates of the farms and herd size, the points were distributed randomly and regularly on the network. Were also simulated the relative initials positions of the focus in a random form on the network, in the center, edges and vertices, considering three areas of study region A. The results showed that there are no difference for the two types network and they confirm the impact of the relative initial position of the focus on the network to a spread of infection in a number of farms, these results were shown when compared to three areas of A.