A Simple Mathematical Model for the Effects of the Growth of Tourism on Environment

Abstract

While many authors have discussed the evolution of tourism flow, few are concerned with how tourism flow starts to evolve and the mechanism behind that evolution. The purpose of this work is to propose a mathematical model that may assist understanding of the mechanism. Assuming basic relationships between the resources, number of visitors and their respective rates of growth, we derive a model defined by two Ordinary Differential Equations whose solutions describe the evolution of both variables in time. As a study case for the model, we use data collected at the Juatinga Ecological Reserve, 23.2o S, 44.5o W , in the State of Rio de Janeiro, Brazil. We conclude that the model fits the data well and the values that can be obtained for the parameters characterize qualitatively the type of visitors