A case study of 2019‐nCoV in Russia using integer and fractional order derivatives

Vellappandi, M.; Kumar, Pushpendra; Govindaraj, V.

doi:10.1002/mma.8736

Cited by 8 publications

(6 citation statements)

References 35 publications

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“…In the works of Baleanu et al [29], Kojabad et al [30], and Qureshi et al [31], fractional extensions of integer-order mathematical models have been proven to be more systematic while representing the natural facts about disease dynamics. At the time of the outbreak of novel coronaviruses, mathematicians have continuously worked on modeling and have come up with many effective mathematical models of integer and fractional order to simulate the transmission of coronaviruses [32][33][34][35][36][37][38][39][40][41][42][43]. In [35], authors have fitted a fractional stochastic model to study the COVID-19 spread in Egypt.…”

Section: Introductionmentioning

confidence: 99%

An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

Baishya,

Achar,

Veeresha

2024

Contemp. Math.

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Vaccination programs aimed at preventing the spread of the coronavirus appear to have a significant global impact. In this research, we have investigated a mathematical model projecting COVID-19 disease spread by considering five groups of individuals viz. vulnerable, exposed, infected, unreported, recovered, and vaccinated. Looking at the current abnormal pattern of the virus spread in the projected model, we have implemented the fractional derivative in the Mittag-Leffler context. Using the existing theory of the fractional derivative, we have examined the theoretical aspects such as the existence and uniqueness of the solutions, the existence and stability of the disease-free and endemic equilibrium points, and the global stability of the disease-free equilibrium point. In computing the basic reproduction number, we have analyzed that the existence and stability of points of equilibrium are dependent on this number. The sensitivity of the basic reproduction number is also examined. The importance of the vaccination drive is highlighted by relating it to the basic reproduction number. Finally, we have presented the simulation of the numerical results by capturing the profile of each group under the influence of the fractional derivative and investigated the impact of vaccination rate and contact rate in controlling the disease by applying the Adams-Bashforth-Moultan (ABM) method. The present research study demonstrates the importance of the vaccination campaign and the curb on individual contact by featuring a novel fractional operator in the projected model and capturing the corresponding consequence.

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Section: Introductionmentioning

confidence: 99%

An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

Baishya,

Achar,

Veeresha

2024

Contemp. Math.

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“…Considering mathematical models with fractional derivatives are effective instruments for researching infectious diseases [21][22][23]. The researchers looked at COVID-19 mathematical models using fractional order derivatives, and the findings were excellent [24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination

Dickson

Padmasekaran

Kumar

2023

Int. J. Dynam. Control

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In this paper, a fractional order nonlinear model for Omicron, known as B.1.1.529 SARS-Cov-2 variant, is proposed. The COVID-19 vaccine and quarantine are inserted to ensure the safety of host population in the model. The fundamentals of positivity and boundedness of the model solution are simulated. The reproduction number is estimated to determine whether or not the epidemic will spread further in Tamilnadu, India. Real Omicron variant pandemic data from Tamilnadu, India, are validated. The fractional-order generalization of the proposed model, along with real data-based numerical simulations, is the novelty of this study.

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“…To date, several real-world problems have been successfully modeled by using various types of fractional derivatives. Here we look at some recent works in this area: In [ 19 ], the authors analyzed the transmission of the COVID-19 epidemic by using integer and fractional derivatives. In [ 20 ], the authors performed the analyses of the existence and uniqueness of a fractional-order blood glucose-insulin minimal model.…”

Section: Introductionmentioning

confidence: 99%

Role of fractional derivatives in the mathematical modeling of the transmission of Chlamydia in the United States from 1989 to 2019

Vellappandi¹,

Kumar

Govindaraj³

2022

Nonlinear Dyn

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Nowadays, the mathematical modeling of infectious diseases is a big trend worldwide. The mathematical models help us to forecast future outbreaks of diseases in the presence of present data. In this article, we represent a model of the transmission of Chlamydia in the United States by using data from 1989 to 2019. In the formulation of the model, we used integer and fractional derivatives. Several graphs are plotted for the various possible cases of the given parameters. The aim of this paper is to justify how the mathematical models in terms of fractional derivatives have more degree of freedom to explore disease dynamics for a particular data set and capture memory effects. The separate parameter estimation for each value of the fractional order increases the novelty of this work. The use of a real-data set of Chlamydia in the United States makes this study more visible and important to the literature.

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A case study of 2019‐nCoV in Russia using integer and fractional order derivatives

Cited by 8 publications

References 35 publications

An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

An Application of the Caputo Fractional Domain in the Analysis of a COVID-19 Mathematical Model

Fractional order mathematical model for B.1.1.529 SARS-Cov-2 Omicron variant with quarantine and vaccination

Role of fractional derivatives in the mathematical modeling of the transmission of Chlamydia in the United States from 1989 to 2019

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