A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms

Zeb, Anwar; Kumar, Pushpendra; Ertürk, Vedat Suat; Sitthiwirattham, Thanin

doi:10.1016/j.jksus.2022.101914

Cited by 31 publications

(23 citation statements)

References 26 publications

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“…A fractional model suggested in [31] has been used to study the infected cases in Argentina. The authors proposed two vaccination models for COVID-19 disease in [33] and presented their numerical simulations. A fractional model for COVID-19 infection with optimal control analysis in [34] has been used to study the infection cases in Spain.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

Khan

Atangana

2022

Physica A: Statistical Mechanics and its Applications

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

Khan

Atangana

2022

Physica A: Statistical Mechanics and its Applications

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“… 7 In Alghamdi et al, 8 the authors used two various fractional derivatives to simulate the dynamics of a 2019‐nCoV model by using real statistical data. Zeb et al 9 have introduced two novel fractional order models containing vaccine terms and solved the models by using various methods, respectively. Some novel control analyses on the spread of 2019‐nCoV by using a model have been given in Misra and Sisodiya.…”

Section: Introductionmentioning

confidence: 99%

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

Vellappandi¹,

Kumar²,

Govindaraj³

2022

Math Methods in App Sciences

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In this article, we define a mathematical model to analyze the outbreaks of the most deadly disease of the decade named 2019‐nCoV by using integer and fractional order derivatives. For the case study, the real data of Russia is taken to perform novel parameter estimation by using the Trust Region Reflective (TRR) algorithm. First, we define an integer order model and then generalize it by using fractional derivatives. A novel optimal control problem is derived to see the impact of possible preventive measures against the spread of 2019‐nCoV. We implement the forward–backward sweep method to numerically solve our proposed model and control problem. A number of graphs have been plotted to see the impact of the proposed control practically. The Russian data‐based parameter estimation along with the proposal of a mathematical model in the sense of Caputo fractional derivative that contains the memory term in the system are the main novel features of this study.

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“…Zeb et al used a piecewise fractional order model of COVID-19 [10]. Zeb et al investigated two different vaccinated fractional order models of COVID-19 by using Caputo-Fabrizio and generalized Caputo operators [11]. FC also has applications in mathematical physics [12], bioengineering [13], and agriculture [14].…”

Section: Introductionmentioning

confidence: 99%

Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System

Ahmad

Rahman

et al. 2022

Mathematics

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Recently, several research articles have investigated the existence of solutions for dynamical systems with fractional order and their controllability. Nevertheless, very little attention has been given to the observability of such dynamical systems. In the present work, we explore the outcomes of controllability and observability regarding a differential system of fractional order with input delay. Laplace and inverse Laplace transforms, along with the Mittage–Leffler matrix function, are applied to the proposed dynamical system in Caputo’s sense, and a general solution is obtained in the form of an integral equation. Then, we set out conditions for the controllability of the underlying model, regarding the linear case. We then expound controllability conditions for the nonlinear case by utilizing the fixed point result of Schaefer and the Arzola–Ascoli theorem. Using the fixed point concept, we prove the observability of the linear case using the observability Grammian matrix. The necessary and sufficient conditions for the nonlinear case are investigated with the help of the Banach contraction mapping theorem. Finally, we add some examples to elaborate on our work.

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A new study on two different vaccinated fractional-order COVID-19 models via numerical algorithms

Cited by 31 publications

References 26 publications

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

Mathematical modeling and analysis of COVID-19: A study of new variant Omicron

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

Controllability and Observability Results of an Implicit Type Fractional Order Delay Dynamical System

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