Análise dos problemas direto e inverso em um modelo de evolução populacional através de transformações integrais e inferência bayesiana

Abstract

Population dynamics models are subject of major relevance, especially when involving human or livestock disease vectors. Such importance is due to the fact that there are several diseases that are spread by some particular species and the knowledge on the behavior of such populations is vital when it is intended to create public policies to control their unbridled proliferation. This work describes a problem of population dynamics with diffusive behavior, with impulsive culling and delayed reproduction. The direct problem describes the space and time evolution of the population density when the model parameters are known and the solution of the partial differential equation is obtained with by the Generalized Integral Transform Technique, a hybrid numerical-analytical approach. However, the direct problem solution does not allow for the analysis of a given species population in a practical application, if the model parameters are not known. In this context, it is proposed in this work the inverse problem formulation and solution through the Bayesian framework for the estimation of the model parameters of a given species population, if experimental data are available.