On the existence and stability of fuzzy CF variable fractional differential equation for COVID-19 epidemic

Verma, Pratibha; Kumar, Manoj

doi:10.1007/s00366-021-01296-9

Cited by 12 publications

(4 citation statements)

References 15 publications

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“…Definition 4. Let D be a mapping such that E × E → R and f, h be two fuzzy number denoted by their parametric form as, g = [f (u), f (u)] and h = [h(u), h(u)] respectively [31]. The Hausdorff distance of g and h is given as,…”

Section: Preliminariesmentioning

confidence: 99%

Study on Viral Transmission Impact on Human Population Using Fractional Order Zika Virus Model

Palanisami,

Elango

2023

IJRCS

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This work comprises the spread of Zika virus between humans and mosquitoes as a mathematical simulation under fractional order, which also incorporates the asymptotically infected human population. For determining the solution of the model the fuzzy Laplace transform technique is utilized. By combining fuzzy logic with the Laplace transform, we can analyze systems even when we lack precise information. Further, the sensitivity analysis is performed to validate the model. On top of that the population dynamics of both human and mosquito populations are discussed using numerical data and the graphical result of the model is presented. The main objective of this work is to study the dynamics of the Zika virus and to examine the effect of virus on humans when the transmission occurs between humans and from mosquitoes, under fractional order. The outcome of these comparisons suggests that even by reducing a minute fractional part of transmission through mosquitoes results in a greater reduction of Zika exposed population. The comparisons improve the understanding of fractional level transmission resulting in more effective drug administration to patients. The Hyers-Ulam stability method is a mathematical technique used to study the stability of functional equations. Eventually, Ulam Hyers and Ulam Hyers Rassias stability are employed to assess the stability of the proposed model.

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Section: Preliminariesmentioning

confidence: 99%

Study on Viral Transmission Impact on Human Population Using Fractional Order Zika Virus Model

Palanisami,

Elango

2023

IJRCS

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“…The dynamics of this type of transmission are described using a fractional order derivative by [27][28][29][30][31][32][33], fractional-order backstepping strategy by Veisi and Delavari [34], generalized fractional-order by Xu et al [35], hybrid stochastic fractional order by Sweilam et al [36], El-Borai and El-Nadi [37], Caputo-Fabrizio (CF) and Atangana-Baleanu models non-singular fractional derivatives by Panwar et al [38], Mohammad and Trounev [39], Peter et al [40], Verma and Kumar [41], Sintunavarat and Turab [42], Kolebaje et al [43], optimized fractional order by Alshomrani et al [44], Caputo-Fabrizio derivative by Baleanu et al [45], fractional Chebyshev polynomials by Hadid et al [46], fractal-fractional order by Algehyne and Ibrahim [47], fractional order with fuzzy theory by Verma and Kumar [48], fractional order derivative with Krasnoselskiiʼs fixed point theorem by Verma et al [49], the multifractional characteristics with time-dependent memory indexes by Jahanshahi et al [50], fractional derivative with Riesz wavelets simulation by Mohammad et al [51]. Padmapriya and Kaliyappan [52], Dong et al [53] discussed the model of fuzzy fractional differential systems for the epidemic.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Santra,

Mahapatra,

Basu

2024

Phys. Scr.

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This article presents an epidemic disease propagation mathematical model in fractional order. The epidemiological characteristics are presented based on the susceptible, exposed, unknown infected, known infected, hospitalized population and the population in the secure zone. Both the disease endemic equilibrium and the disease-free equilibrium's stability characteristics have been examined using the basic reproduction number. Variation of basic reproduction number based on the different sensitive parameters has been discussed. It has been disputed whether the fractional model provides a uniform, reliable solution. An analysis of the time history of unknown and known infected populations, hospitalized populations and recovered populations at different values of various sensitive parameters has been carried out. To support the key theoretical conclusions, some numerical simulations are completed using MATLAB. The impact of various populations on the propagation of the illness has also been investigated, as well as how specific state variables change over time for various fractional order values.

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“…Some novel theoretical results related to the existence and stability of the fuzzy‐type 2019‐nCoV model in terms of Caputo–Fabrizio derivative have been derived in Verma and Kumar. 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.…”

Section: Introductionmentioning

confidence: 99%

“…Ahmad et al 6 proposed a strong and efficient model to justify the dynamics of 2019‐nCoV. Some novel theoretical results related to the existence and stability of the fuzzy‐type 2019‐nCoV model in terms of Caputo–Fabrizio derivative have been derived in Verma and Kumar 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.…”

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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On the existence and stability of fuzzy CF variable fractional differential equation for COVID-19 epidemic

Cited by 12 publications

References 15 publications

Study on Viral Transmission Impact on Human Population Using Fractional Order Zika Virus Model

Study on Viral Transmission Impact on Human Population Using Fractional Order Zika Virus Model

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

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

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