Equações diferenciais ordinárias e o modelo de Malthus: uma tentativa de melhoria nas predições de dinâmica populacional

Abstract

Considering the importance of the Malthusian model in the context of population modeling and the error that arises from its application when it comes to human populations, research is done on the efficiency of the Malthus model in order to investigate the possibility of a combination of 𝑃0 and 𝑘 in accuracy of the Model in the population dynamics of Uruçuí-PI for the year 2020 based on the effectiveness of the model when applied to the population dynamics of other cities in the South of Piauí. To this end, we performed a description of the Malthus Model and its application in the population dynamics of the municipalities of Bom Jesus, Canto do Buriti, São João, Corrente, Eliseu Martins, Bertolínia, Baixa Grande do Ribeiro and Marcos Parente, both belonging to the state of Piauí. Considering the effectiveness presented by the model, we applied the model to the population dynamics of Uruçuí. Then, a bibliographic research about differential equations and the studied model is provided, as well as the collection of the required population data. Given this, it appears that there is an evident distortion between the actual and predicted data, a reduction in error is noted when applied to the initial population of 1991 and using a constant proportionality 𝑘3 in the cities of Bom Jesus, Canto do Buriti , São João, Corrente, Eliseu Martins, Bertolínia, Baixa Grande do Ribeiro and Marcos Parente, and that there is a significant approximation between the prediction and the real data of the population of Uruçuí, which imposes the observation that it is possible, through the pair P (t_0) = 15661 (population in the year 1991) and 𝑘3 (found using the 1991 and 2010 censuses) to improve the description of population growth in the aforementioned municipality.