The memory effect on fractional calculus: an application in the spread of COVID-19

Barros, Laécio Carvalho de; Lopes, Michele Martins; Pedro, Francielle Santo; Esmi, Estevão; Santos, José Paulo Carvalho dos; Sánchez, Daniel Eduardo

doi:10.1007/s40314-021-01456-z

Cited by 85 publications

(60 citation statements)

References 20 publications

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“…Note that model ( 7 ) has no endemic equilibrium, so the only constant solution exists is free disease equilibrium, but if we do not neglect the effect of vital dynamics, the model must have endemic equilibrium, some works that deal with COVID-19 and other infectious diseases without endemic equilibrium are found in de Barros et al. ( 2021 ), Watve et al. ( 2021 ), Ram and Schaposnik ( 2021 ), Da Silva ( 2021 ) and Gao et al.…”

Section: Global Stability Of the Equilibriamentioning

confidence: 99%

Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco

et al. 2022

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In December 2019, in Wuhan, China, a new disease was detected, and the virus easily spread throughout other nations. March 2, 2020, Morocco announced 1st infection of coronavirus. Morocco verified a total of 653,286 cases, 582,692 recovered, 60,579 active case, and 10,015 as confirmatory fatalities, as of 4 August 2021. The objective of this article is to study the mathematical modeling of undetected cases of the novel coronavirus in Morocco. The model is shown to have disease-free and an endemic equilibrium point. We have discussed the local and global stability of these equilibria. The parameters of the model and undiscovered instances of COVID-19 were assessed by the least squares approach in Morocco and have been eliminated. We utilized a Matlab tool to show developments in undiscovered instances in Morocco and to validate predicted outcomes. Like results, until August 4, 2021, the total number of infected cases of COVID-19 in Morocco is 24,663,240, including 653,286 confirmed cases, against 24,009,954 undetected. Further, our approach gives a good approximation of the actual COVID-19 data from Morocco and will be used to estimate the undetected cases of COVID-19 in other countries of the world and to study other pandemics that have the same nature of spread as COVID-19.

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Section: Global Stability Of the Equilibriamentioning

confidence: 99%

Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco

et al. 2022

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“…In Figure 4, we consider different values for α and the initial conditions x 0 from (12). The global stability of the disease free equilibrium (10) is illustrated in Figure 5, considering different initial conditions x i , i = 0, . .…”

Section: A Modified Fractional Sica Model For Hiv/aidsmentioning

confidence: 99%

“…For example, Refs. [10][11][12] proposed fractional epidemiological models to study the spread of COVID-19 in different countries, Refs. [13,14] investigated the HIV infection, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

Almeida¹,

Martins²,

Silva³

2021

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In this paper, we present a new result that allows for studying the global stability of the disease-free equilibrium point when the basic reproduction number is less than 1, in the fractional calculus context. The method only involves basic linear algebra and can be easily applied to study global asymptotic stability. After proving some auxiliary lemmas involving the Mittag–Leffler function, we present the main result of the paper. Under some assumptions, we prove that the disease-free equilibrium point of a fractional differential system is globally asymptotically stable. We then exemplify the procedure with some epidemiological models: a fractional-order SEIR model with classical incidence function, a fractional-order SIRS model with a general incidence function, and a fractional-order model for HIV/AIDS.

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“…Nesta seção mostramos o efeito de memória (ou, mais especificamente, efeito de histerese) no cálculo fracionário via teoria estatística, que até onde sabemos, foi feito pela primeira vez pelos autores em [1]. Isto será feito através da integral e das derivadas fracionárias de uma função f .…”

Section: Preliminaresunclassified

“…Demonstração. Pode ser encontrada em [1]. 10), para 0 < α < 1, podemos reescrever a derivada de Caputo como segue:…”

Section: Preliminaresunclassified

Sobre o efeito de memória no cálculo fracionário

Lopes¹,

Pedro²,

Esmi³

et al. 2021

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. O cálculo fracionário tem sido bastante utilizado na modelagem de problemas reais. Ele apresenta, como sua principal vantagem, o efeito de memória na dinâmica do sistema. O objetivo deste trabalho é, através de uma abordagem estatística, atestar tal efeito de memória neste cálculo. Mais especificamente, o efeito de histerese. Além disso, analisamos a contribuição dos valores históricos de uma função na aplicação dos operadores fracionários. Por fim, para ilustrar a eficiência dessa ferramenta na modelagem matemática, realizamos uma aplicação a fim de compará-la com o cálculo clássico.

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The memory effect on fractional calculus: an application in the spread of COVID-19

Cited by 85 publications

References 20 publications

Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco

Analysis and dynamics of a mathematical model to predict unreported cases of COVID-19 epidemic in Morocco

Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

Sobre o efeito de memória no cálculo fracionário

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