Impact of awareness program on diabetes mellitus described by fractional-order model solving by homotopy analysis method

Mollah, Saddam; Biswas, Santosh; Khajanchi, Subhas

doi:10.1007/s11587-022-00707-3

Cited by 10 publications

(3 citation statements)

References 44 publications

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“…A fractional-order derivative [122] for a complex system of glucose-insulin regulation; [123] employed the Atangana-Baleanu derivative to analyze the fractional optimal control model for COVID-19 and diabetes co-dynamics. The study of a model for diabetes awareness that is created by a nonlinear interaction between the number of diabetes patients and the cumulative density of awareness-raising campaigns is illustrated by [124], which shows potential results. The novel fractional for glucose-insulin regulatory system on diabetes mellitus using the Atangana Baleanu-Caputo derivative along with stability results was explored by researchers [125].…”

Section: Contribution Of Fractional On Epidemic Modelmentioning

confidence: 99%

Untitled

2023

Progr. Fract. Differ. Appl.

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Both mathematics and science are important for one another and have a close relationship. It is impossible to dispute the significance of mathematics in a number of scientific disciplines, including electrical engineering, physics, biology, and medicine. Due to a number of applications of mathematical biology in the twenty-first century, researchers have taken a special interest in this field. Due to the complexity of the underlying connections, both deterministic and stochastic epidemiological models are founded on an inadequate understanding of the infectious network. Over the past several years, the use of different fractional operators to model the problem has grown, and it is now a common way to study how epidemics spread. New fractional operators, the infectious disease model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's local and global stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical technique to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the purposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. Infectious disease fractional order model is offered for analysis with simulations in order to determine the possible efficacy of disease transmission in the Community. The Fractal fractional operator is employed to study the dynamical transmission of diseases effect on society which is helpful for analysis, decision making, and disease control. Are treated with the Banach contraction principle. Microorganisms, interactions between individuals or groups, and environmental, social, economic, and demographic factors on a broader scale are all examples. Finally, numerical simulations that demonstrate the impact of fractional parameters on our found solutions are built to study the impact of the system parameter on the disease's spread. In conclusion, fractional operators in mathematical models can help decision-makers make better choices regarding the course of action to take in an epidemic situation. Further, we suggested some future work directions with the help of the new hybrid fractional operator. Fractional Calculus is a prominent topic for research within the discipline of Applied Mathematics due to its usefulness in solving problems in many different branches of science, engineering, and medicine. Recent researchers have identified the importance of mathematical tools in various disease models as being very useful to study the dynamics with the help of fractional and integer calculus modeling.

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Section: Contribution Of Fractional On Epidemic Modelmentioning

confidence: 99%

Untitled

2023

Progr. Fract. Differ. Appl.

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“…However, the researcher was able to prove the convergence of HAM [31]. This method has been successfully applied to solve many types of linear and nonlinear problems [1,13,14,16,30,32,33,38,45], In 2020, researchers were able to solve Two-Dimensional nonlinear Volterra-Fredholm fuzzy integral equations by HAM [15]. Also, others were able to solve Mixed Volterra-Fredholm integro-differential equations using same method [16].…”

Section: Introductionmentioning

confidence: 99%

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

Ahmed¹,

Al-Hayani

Al-Bayati³

2023

Eur. J. Pure Appl. Math.

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This paper presents the application of the Homotopy Analysis Method (HAM) for solving nonlinear system of Volterra integral equations used to obtain a reasonably approximate solution. The HAM contains the auxiliary parameter h which provides a simple way to adjust and control the convergence region of the solution series. The results show that the HAM is a very effective method as well. The results were compared with the solutions obtained by developing a homotopy analysis method using the genetic algorithm (HAM-GA), considering the residual error function as a fitness function of the genetic algorithm.

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“…Their findings demonstrated that a public awareness campaign could reduce the prevalence of diabetes mellitus. Additionally, Mollah et al created a model centered on interactions between the density of diabetes awareness programs and the number of diabetic patients [11].…”

mentioning

confidence: 99%

An Analysis of the Effects of Lifestyle Changes by Using a Fractional-Order Population Model of the Overweight/Obese Diabetic Population

Albalawi,

Malik,

Alkahtani

et al. 2023

Fractal Fract

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Unbalanced lifestyles and other underlying medical conditions are responsible for the worrying pace at which diabetes mellitus is becoming a global health crisis. Recent studies suggest that placing a diabetic patient into remission through a rigorous lifestyle change program can normalize blood glucose levels. This research focuses on fractional order derivative-based mathematical modeling and analysis of the diabetes mellitus model with remission parameters. Firstly, the existence and uniqueness of the solution of the diabetes mellitus model are discussed. Non-negativity and boundedness are also examined. Afterward, the concept of the Jacobian matrix is used to investigate the stability of the model’s equilibrium points. The Daftardar-Gejji and Jafari Method has finally been applied to approximate the solutions. The conclusions drawn from numerical simulations of the diabetic model with fractional-order derivatives show a clear dependence on the remission parameters and fractional-order derivative.

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Impact of awareness program on diabetes mellitus described by fractional-order model solving by homotopy analysis method

Cited by 10 publications

References 44 publications

Untitled

Untitled

The Homotopy Analysis Method to Solve the Nonlinear System of Volterra Integral Equations and Applying the Genetic Algorithm to Enhance the Solutions

An Analysis of the Effects of Lifestyle Changes by Using a Fractional-Order Population Model of the Overweight/Obese Diabetic Population

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