ABSTRACT The curve of cumulative cases of individuals infected by COVID-19 shows similar growth to the logistic curve in the period referring to each epidemic “wave”, as each peak of active cases is called. Considering that in pandemic scenarios it is common to seek control measures based on previous experiences, in this paper we model the curve of cumulative cases through a logistic model with infected removal to include the control measures in the dynamics. This model is based on fractional differential equations to also include the memory effect. We study the scenario of the first two “waves” in the analyzed countries: Brazil, China, Italy, and Switzerland. Scenarios with and without control measures are compared, proving the importance of control measures such as isolation. Moreover, this model makes it possible to determine the portion of the population that did not participate in the dynamics of the spread of the disease, as well as to analyze how the number of infected people reduced in each country.

RESUMO Nessa proposta estudamos e definimos uma integral fuzzy adaptada, baseada na integral de Sugeno. Ademais, apresentamos uma fórmula de integração numérica que aproxima o valor da integral fuzzy adaptada. Assim, provamos que a integral de Riemann e a integral fuzzy adaptada são equivalentes para funções potência. Logo, aplicamos a fórmula proposta na integração numérica, requerida no método de elementos finitos, para obter uma solução aproximada de um problema de valor de contorno para a equação de Poisson unidimensional. Finalmente, observamos melhores resultados na solução aproximada obtida com o uso da nossa fórmula quando comparada com a regra simples de trapézio.

ABSTRACT In this paper we study and define an adapted fuzzy integral, based on the Sugeno integral. Moreover, we present a numerical integration formula which approximates the value of the adapted fuzzy integral. Thus, we prove that the Riemann integral and the adapted fuzzy integral are equivalent for power functions. Next, we apply the formula proposed in the numerical integration, required in the finite element method, to obtain a numerical solution of a boundary value problem for the one-dimensional Poisson equation. Finally, we observed better results of the approximate solution obtained in the example with the use of our formula when compared with the simple trapezoidal rule.