Existence Theory and Novel Iterative Method for Dynamical System of Infectious Diseases

Ali, Gauhar; Nazir, Ghazala; Shah, Kamal; Li, Yongjin

doi:10.1155/2020/8709393

Cited by 5 publications

(2 citation statements)

References 35 publications

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“…For this purpose numerous techniques have been established to handle the problems. Integral transform when coupled with perturbations or decompositions techniques, we get hybrid method which have been increasingly used to handle linear and nonlinear problems of fractional order, for detail see [8] , [9] , [10] , [11] , [12] , [13] , [17] , [18] , [23] , [29] , [31] , [32] , [33] , [34] , [35] , [36] , [37] . The study of COVID-19 mathematical model under the fractional order operators is also considered in last few months.…”

Section: Introductionmentioning

confidence: 99%

Study of COVID-19 mathematical model of fractional order via modified Euler method

Nazir

Zeb

Shah

et al. 2021

Alexandria Engineering Journal

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Our main goal is to develop some results for transmission of COVID-19 disease through Bats-Hosts-Reservoir-People (BHRP) mathematical model under the Caputo fractional order derivative (CFOD). In first step, derived the feasible region and bounded ness of the model. Also, we derived the disease free equilibrium points (DFE) and basic reproductive number for the model. Next, we establish theoretical results for the considered model via fixed point theory. Further, the condition for Hyers-Ulam’s (H-U) type stability for the approximate solution is also established. Then, we compute numerical solution for the concerned model by applying the modified Euler’s method (MEM). For the demonstration of our proposed method, we provide graphical representation of the concerned results using some real values for the parameters involve in our considered model. For numerical illustration, we use Matlab.

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Section: Introductionmentioning

confidence: 99%

Study of COVID-19 mathematical model of fractional order via modified Euler method

Nazir

Zeb

Shah

et al. 2021

Alexandria Engineering Journal

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“…Recently, new fractional operators were developed that give a precise description of memory and have succeeded with regards to modeling infectious ailments; see [20][21][22]. The worldwide issue of the spread of the ailment attracted the consideration of analysts from different fields, which prompted the rise of various propositions to examine and predict the development of the epidemic [23,24].…”

Section: Introductionmentioning

confidence: 99%

Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo–Fabrizio derivative

2021

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This manuscript is devoted to a study of the existence and uniqueness of solutions to a mathematical model addressing the transmission dynamics of the coronavirus-19 infectious disease (COVID-19). The mentioned model is considered with a nonsingular kernel type derivative given by Caputo–Fabrizo with fractional order. For the required results of the existence and uniqueness of solution to the proposed model, Picard’s iterative method is applied. Furthermore, to investigate approximate solutions to the proposed model, we utilize the Laplace transform and Adomian’s decomposition (LADM). Some graphical presentations are given for different fractional orders for various compartments of the model under consideration.

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Investigation of Fractional-Ordered Tumor-Immune Interaction Model via Fractional-Order Derivative

ALI,

MARWAN,

RAHMAN

et al. 2024

Fractals

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Dynamical analysis of system of ordinary differential equations (ODEs) is an interesting topic among researchers and several tools have been discovered since so far to deal with its several other features. There are many built-in functions designed in MATLAB that researchers can use as a tool for the system of ODEs with integer order but in the similar systems have fractional-order derivative is a difficult task. Therefore, the purpose of this work is to use the Caputo fractional-order derivative to qualitatively analyze and then numerically simulate the tumor-immune system interaction model. Moreover, the Schauder fixed point theorem is used to establish the condition for the existence of at least one solution, while the Banach fixed point theorem is utilized to guarantee the existence of a unique solution. Moreover, the stability in the trajectories of considered system achieved with the aid of Ulam–Hyers (UH) stability. In addition, the numerical computations are performed using Variational Iteration Method (VIM) and the visualized results are shown using MATLAB.

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Existence Theory and Novel Iterative Method for Dynamical System of Infectious Diseases

Cited by 5 publications

References 35 publications

Study of COVID-19 mathematical model of fractional order via modified Euler method

Study of COVID-19 mathematical model of fractional order via modified Euler method

Theoretical and numerical analysis for transmission dynamics of COVID-19 mathematical model involving Caputo–Fabrizio derivative

Investigation of Fractional-Ordered Tumor-Immune Interaction Model via Fractional-Order Derivative

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