Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis

Berhe, Hailay Weldegiorgis; Qureshi, Sania; Shaikh, Asif Ali

doi:10.1016/j.chaos.2019.109536

Cited by 24 publications

(14 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[16][17][18][19][20][21][22][23][24][25][26] Very recently, the application of this concept was extended to capture chaotic attractors and even to describe the spread of infectious diseases within a given population. [27][28][29][30][31][32][33][34][35][36][37] The results obtained from these studies were similar to those obtained from classical fractional differential and integral operators, a proof and validity of nonlocality of this calculus more precisely the associate integral display properties similar to those of the Riemann-Liouville integral. While, in the literature, there are some published articles where these differential operators are discredited even, in this article, it is claimed that they are not differential operators; the results obtained from models show that the differential operators appear in many situations in nature.…”

Section: Introductionsupporting

confidence: 76%

“…Some more applications of this concept can be found in diffusion, groundwater flow problem, and groundwater pollution problems 16–26 . Very recently, the application of this concept was extended to capture chaotic attractors and even to describe the spread of infectious diseases within a given population 27–37 . The results obtained from these studies were similar to those obtained from classical fractional differential and integral operators, a proof and validity of nonlocality of this calculus more precisely the associate integral display properties similar to those of the Riemann‐Liouville integral.…”

Section: Introductionmentioning

confidence: 56%

“…12A-F, 13A-F, and 14A-F show numerical simulations for the four-dimensional system in Atangana-Baleanu-Caputo sense(29) considering different values of and , arbitrarily chosen.…”

mentioning

confidence: 99%

“…Numerical results for the four-dimensional system(29) considering the fractal-fractional derivative in the Atangana-Baleanu-Caputo sense and the numerical scheme given by Equation(30)for a = −1.05, b = 0.7, c = −0.19, e = 1.37, f = 1.79, = −0.2, step size h = 1 × 10 −4 , simulation time t = 200 s, and initial conditions x(0) = −10, y(0) = 0.1, z(0) = 0.1, and w(0) = 0.1, for = 0.85 and = 0.95…”

mentioning

confidence: 99%

See 3 more Smart Citations

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Gómez‐Aguilar

Atangana

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

Very recently, the concept of fractal differentiation and fractional differentiation has been combined to produce new differentiation operators. The new operators were constructed using three different kernels, namely, power law, exponential decay, and the generalized Mittag‐Leffler function. The new operators have two parameters: the first is considered as fractional order and the second as fractal dimension. In this work, we applied these new operators to model some chaotic attractors, and the models were solved numerically using a new and very efficient numerical scheme. We presented numerical simulations for some specific fractional order and fractal dimension. The classical fractional differential models could be recovered when the fractal dimension is equal to 1; in these cases, the obtained attractors with power law presented no similarities. Nevertheless, those obtained via Caputo‐Fabrizio and the Atangana‐Baleanu derivative show some crossover effects, which is due to non‐index law property. However, those obtained from fractal‐fractional, in particular, those with the Mittag‐Leffler kernel, show very strange and new attractors with self‐similarities; these results are obtained for the first time. We conclude that this new concept is the future to modelling complexities with self‐similarities.

show abstract

Section: Introductionsupporting

confidence: 76%

Section: Introductionmentioning

confidence: 56%

“…12A-F, 13A-F, and 14A-F show numerical simulations for the four-dimensional system in Atangana-Baleanu-Caputo sense(29) considering different values of and , arbitrarily chosen.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Gómez‐Aguilar

Atangana

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Fractional order dynamical systems appear in several works, especially in viscoelasticity and in hereditary solid mechanics. Recently, various practical applications of the fractional calculus using Caputo fractional derivative has been addressed by Qureshi et al in [6,33,34,35,36]. Considerable work has been done in the area of fractional optimal control problem on the real line.…”

mentioning

confidence: 99%

Fractional optimal control problems on a star graph: Optimality system and numerical solution

Mehandiratta¹,

Mehra²,

Leugering³

2021

Mathematical Control &Amp; Related Fields

View full text Add to dashboard Cite

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

et al. 2022

View full text Add to dashboard Cite

The deadly outbreak of the second wave of Covid-19, especially in worst hit lower-middle-income countries like India, and the drastic rise of another growing epidemic of Mucormycosis , call for an efficient mathematical tool to model pandemics, analyse their course of outbreak and help in adopting quicker control strategies to converge to an infection-free equilibrium. This review paper on prominent pandemics reveals that their dispersion is chaotic in nature having long-range memory effects and features which the existing integer-order models fail to capture. This paper thus puts forward the use of fractional-order (FO) chaos theory that has memory capacity and hereditary properties, as a potential tool to model the pandemics with more accuracy and closeness to their real physical dynamics. We investigate eight FO models of Bombay plague, Cancer and Covid-19 pandemics through phase portraits, time series, Lyapunov exponents and bifurcation analysis. FO controllers (FOCs) on the concepts of fuzzy logic, adaptive sliding mode and active backstepping control are designed to stabilise chaos. Also, FOCs based on adaptive sliding mode and active backstepping synchronisation are designed to synchronise a chaotic epidemic with a non-chaotic one, to mitigate the unpredictability due to chaos during transmission. It is found that severity and complexity of the models increase as the memory fades, indicating that FO can be used as a crucial parameter to analyse the progression of a pandemic. To sum it up, this paper will help researchers to have an overview of using fractional calculus in modelling pandemics more precisely and also to approximate, choose, stabilise and synchronise the chaos control parameter that will eliminate the extreme sensitivity and irregularity of the models.

show abstract

Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis

Cited by 24 publications

References 33 publications

New chaotic attractors: Application of fractal‐fractional differentiation and integration

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Fractional optimal control problems on a star graph: Optimality system and numerical solution

Is fractional-order chaos theory the new tool to model chaotic pandemics as Covid-19?

Contact Info

Product

Resources

About