Modelagem matemática aplicada ao crescimento populacional e de uma atividade econômica (suinocultura) da cidade de Tupãssi / PR

Abstract

In this work a study on population growth over time and weight gain of pigs from a swine farm, both from the city of Tupãssi/PR, was carried out through Mathematical Modeling. From the existing models in the literature, the Malthus model and the Verhulst model for population modeling and the Gompertz model and the Montroll model for swine growth were chosen. The work began with the study of the models be used, and later the data collections were performed. First, the population data were taken from the official website of the Brazilian Institute of Geography and Statistics (IBGE). Subsequently, swine data were collected from a domestic pig farming in the city, which is an important industrial producer in the region. Then, computer simulations were made for the elected models and a comparison of the data obtained with the empirical data. Relative error was used to validate the results and it can be concluded that the model that best suits the population growth of Tupãssi is the Verhulst model. For swine growth it was validated by means of relative error means and a brief comparison of the standard deviations of the models with the empirical data, thus concluding that the model that best describes this growth is the Gompertz model.