The Use of Triangular Norms in Epidemiological Models: A Comparative Study Using COVID-19 Data

Lopes, Michele Martins; Simoes, Francielle Santo Pedro; Esmi, Estevão; Barros, Laécio Carvalho de

doi:10.1109/tfuzz.2022.3205357

Cited by 1 publication

(5 citation statements)

References 11 publications

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“…In [1,5] it is possible to see formulas that relate Riemann-Liouville fractional derivative and integral operators with weighted averages of historical values as well.…”

Section: Results On Caputo Fractional Derivativementioning

confidence: 99%

“…In the works [1,5] the authors used Caputo fractional derivative to include the memory effect in the SIR (Susceptible-Infected-Recovered) epidemiological model, obtaining the following system.…”

Section: Fractional Sir Model: An Application To Covid-19mentioning

confidence: 99%

“…In [1,5] the authors compare the classic version of the SIR model with the fractional version (with memory) to describe active cases of COVID-19 in some countries, using least squares data fit for both models. In this subsection, we recall the results obtained by them, to emphasize the advantage of using the Caputo derivative in epidemiological models, and we use these results as an example to identify the memory effect through the order α of the fractional derivative.…”

Section: Greater Efficiency Of the Fractional Model And The Memory Ef...mentioning

confidence: 99%

“…In [1,5] it was shown that the fractional model is a good tool to study the phenomenon when there is a memory effect in the process. In Figures 3 and 4, we see the results obtained for the first "wave" of China and South Korea, where the actual data are represented by the blue dots, the solution of the classic model is given by the black continuous curve and the solution of the fractional model is given by the red dashed curve.…”

Section: Greater Efficiency Of the Fractional Model And The Memory Ef...mentioning

confidence: 99%

“…The main objective of this work is, after remembering the equation that indicates the memory effect in the Caputo derivative published by the authors in [1,5], to show three interesting results that we can obtain from this formula: the explicit elaboration of the dimensional analysis of the fractional derivative, the possibility of observing how the weighted average works and, finally, the fact that the Caputo derivative is not zero at the critical point of the function. We do this in Section 2 and we illustrate the results in Section 3, using an application also already made by the authors in [1,5], with the SIR epidemiological model to study active cases of COVID-19.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Caputo Derivative as Weighted Average of Historical Values: some consequences illustrated via COVID-19 data

Lopes,

Pedro,

Leite

et al. 2023

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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This paper uses the formula previously proposed by the authors themselves, in which the Caputo fractional derivative is written proportionally to the weighted average of historical values of the classical derivative (Equation ( 2)). Three consequences of this formula are treated in this work. The first explicitly shows the dimension of the Caputo derivative, the second indicates which historical values of the classical derivative have greater/lower weight for the Caputo operator at the current instant, and finally, the third shows that the Caputo derivative is zero at instants after the critical point occurred (allowing interpretations for the order of the derivative, for example in the dynamics of some disease). To illustrate these three results, we used examples previously obtained by the authors themselves, modeling the curve of active COVID-19 cases with the SIR model. This approach captures the memory effect well in epidemiological models.

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“…In [1,5] it is possible to see formulas that relate Riemann-Liouville fractional derivative and integral operators with weighted averages of historical values as well.…”

Section: Results On Caputo Fractional Derivativementioning

confidence: 99%

Section: Fractional Sir Model: An Application To Covid-19mentioning

confidence: 99%

Section: Greater Efficiency Of the Fractional Model And The Memory Ef...mentioning

confidence: 99%

Section: Greater Efficiency Of the Fractional Model And The Memory Ef...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Caputo Derivative as Weighted Average of Historical Values: some consequences illustrated via COVID-19 data

Lopes,

Pedro,

Leite

et al. 2023

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

The Use of Triangular Norms in Epidemiological Models: A Comparative Study Using COVID-19 Data

Cited by 1 publication

References 11 publications

Caputo Derivative as Weighted Average of Historical Values: some consequences illustrated via COVID-19 data

Caputo Derivative as Weighted Average of Historical Values: some consequences illustrated via COVID-19 data

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