Fractional order SIR model with generalized incidence rate

Khan, Muhammad Altaf; Ismail, Muhammad; Ullah, Saif; Farhan, Muhammad

doi:10.3934/math.2020124

Cited by 30 publications

(9 citation statements)

References 20 publications

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“…The SIR system is the simplest of the compartmental models used for the mathematical modeling of infectious diseases and had been solved numerically using various approaches, including Monte Carlo methods, wavelets, fuzzy control etc [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and approximate solutions had been proposed [28,29]. The considered population of N 1 initially unrecovered/unremoved persons is assigned to the three compartments S (susceptible), I (infectious), or R (recovered/removed).…”

Section: Introductionmentioning

confidence: 99%

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Schlickeiser

Kröger

2021

J. Phys. A: Math. Theor.

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Section: Introductionmentioning

confidence: 99%

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Schlickeiser

Kröger

2021

J. Phys. A: Math. Theor.

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“…Fractional operators have received increasing interest by several directions in the modeling of biological process. Let us brefly review one of the recent papers, in [34] for exemple, the authors proposed and studied the dynamics behavior of COVID-19, that was by analysed an SEIHDR model based on ABC operator, they showed the transmission dynamics of COVID-19 after they analysed the existence results, see [1,2,13,12,11,21,8,7,6,18,19,20,16,10,9,23,24,29,31,32,33] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A Fractional Epidemic Model with Mittag-Leffler Kernel for COVID-19

Aghdaoui¹,

Tilioua²,

Nisar³

et al. 2021

Math.Biol.Bioinf.

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The aim is to explore a COVID-19 SEIR model involving Atangana-Baleanu Caputo type (ABC) fractional derivatives. Existence, uniqueness, positivity, and boundedness of the solutions for the model are established. Some stability results of the proposed system are also presented. Numerical simulations results obtained in this paper, according to the real data, show that the model is more suitable for the disease evolution.

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“…In recent years, mathematical models with FO derivatives have been studied for deeper understanding of the problem under consideration as can be found in the literature and references therein [16,17]. A fractional SIR epidemic involving generalized incidence rate is recently studied in [18]. Indeed, very few FO models of HIV/AIDS have been considered in many epidemiological models.…”

Section: Introductionmentioning

confidence: 99%

Modeling and analysis of the dynamics of HIV/AIDS with non-singular fractional and fractal-fractional operators

Ullah

Khan

et al. 2021

Phys. Scr.

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In the present study, we analyze the dynamics of HIV/AIDS epidemic model with fractional and the new definition of a nonlocal fractal-fractional derivative in the Atangana-Baleanu-Caputo (ABC) sense. The proposed model is initially formulated with the help of classical integer-order differential equations and then the ABC fractional derivative is used to obtain the fractional HIV/AIDS model with arbitrary order p 1 . Then we present some basic properties including equilibria and the basic reproduction number of the model. The local and global stability of the fractional model at disease free equilibrium is shown and it is found that the model is stable when the threshold quantity is less than 1. Further, an efficient numerical approach is applied to present an iterative scheme for the fractional model and present graphical results for various values of p 1 . After this, we make use of the new fractalfractional operator to formulate the HIV/AIDS model in the ABC sense. The uniqueness and existence of the solutions are shown through the Picard-Lindelof theorem. Furthermore, we derive an iterative scheme of the fractal-fractional ABC model using a novel numerical method based on Adams-Bashforth fractal-fractional approachand depicts detailed graphical results for many values of fractional and fractal orders p 1 and p 2 respectively. The simulation results show that the HIV/AIDS model with the novel fractal-fractional operator provides biologically more feasible analysis than that of the classical fractional and integer-order models.

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Fractional order SIR model with generalized incidence rate

Cited by 30 publications

References 20 publications

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

A Fractional Epidemic Model with Mittag-Leffler Kernel for COVID-19

Modeling and analysis of the dynamics of HIV/AIDS with non-singular fractional and fractal-fractional operators

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