Modelos sigmoidais e suas aplicações
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Data
2022-01-20
Autores
Carmo, Victor Matheus Silva do
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Universidade Estadual Paulista (Unesp)
Resumo
Modelos sigmoidais são utilizados para descrever curvas de crescimento em
forma de S, constituídos por funções reais limitadas, diferenciáveis e definidas para
todos os valores reais. Uma função sigmóide é monotônica, diferenciável, possuindo
um único ponto de inflexão e derivada primeira com gráfico em forma de sino. Dentre
as várias funções sigmoidais existentes, foram apresentadas cinco neste trabalho,
sendo a função Logística, de Gompertz, de Richards, de Morgan-Mercer-Flodin e de
Weibull. Estudou-se três aplicações de funções sigmoidais, sendo estas aplicações a
análise da Atividade Metanogênica Específica de Lodos Anaeróbios, a análise cinética
de transformação de fase no estado sólido e a análise do número de casos
acumulados de infectados de COVID-19 no Brasil durante o período de 25/02/2020 a
07/12/2021, sendo esta última aplicação sob a hipótese que a taxa de infectados é
proporcional ao número de suscetíveis e à disseminação no vírus como uma função
potência do tempo.
Sigmoidal models are used to describe S-shaped growth curves, consisting of limited real functions, differentiable and defined for all real values. A sigmoid function is monotonic, differentiable, having a single inflection point and a first derivative with a bell-shaped graph. Among the several existing sigmoidal functions, five were found in this work, being the Logistic function, of Gompertz, Richards, Morgan-Mercer-Flodin and Weibull. Three applications of sigmoidal functions were studied, these applications being an analysis of the Specific Methanogenic Activity of Anaerobic Sludges, a kinetic analysis of phase transformation in the solid state and the analysis of the number of accumulated cases of COVID-19 infected in Brazil during the period from 25/02/2020 to 07/12/2021, the latter being applied under the assumption that an infected rate is proportional to the number of susceptibles and the spread in the virus as a function of time.
Sigmoidal models are used to describe S-shaped growth curves, consisting of limited real functions, differentiable and defined for all real values. A sigmoid function is monotonic, differentiable, having a single inflection point and a first derivative with a bell-shaped graph. Among the several existing sigmoidal functions, five were found in this work, being the Logistic function, of Gompertz, Richards, Morgan-Mercer-Flodin and Weibull. Three applications of sigmoidal functions were studied, these applications being an analysis of the Specific Methanogenic Activity of Anaerobic Sludges, a kinetic analysis of phase transformation in the solid state and the analysis of the number of accumulated cases of COVID-19 infected in Brazil during the period from 25/02/2020 to 07/12/2021, the latter being applied under the assumption that an infected rate is proportional to the number of susceptibles and the spread in the virus as a function of time.
Descrição
Palavras-chave
COVID-19, Função sigmoidal, Atividade metanogênica específica, Lodos anaeróbios