Fractional-order delayed Ross–Macdonald model for malaria transmission

Cui, Xinshu; Xue, Dingyü; Li, Tingxue

doi:10.1007/s11071-021-07114-7

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…To examine the consequences of heterogeneous vector biting exposure on the human population, researchers [105] developed and tested a fractional-order model for malaria disease transmission utilizing the Atangana-Baleanu derivative in Caputo sense. The nonlinear delayed Ross-Macdonald model for malaria transmission was generalized to a unique fractional-order model in [106], which improved the dynamics and added complexity. A stochastic model for co-infection with pneumonia and typhoid was published in [107] to examine the varied connections between the two diseases under the effect of preventative measures that consider environmental noise and piecewise fractional derivative operators, as well as some applications in [108].…”

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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“…They proposed a fractional extension of the multistage differential transform method to model toxoplasmosis. Cui et al [ 33 ] investigated the dynamics of Plasmodium using a time-delayed fractional-order Ross-Macdonald model for transmission periods of malaria and the order of its dynamic behavior. Abdullah et al [ 34 ] solved a fractional temporal SEIR measles model composed of four-time fractional ordinary differential equations (TFODEs) in three stages.…”

Section: Introductionmentioning

confidence: 99%

A study on fractional tumor-immune interaction model related to lung cancer via generalized Laguerre polynomials

Hassani,

Avazzadeh,

Agarwal

et al. 2023

BMC Med Res Methodol

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Background Cancer, a complex and deadly health concern today, is characterized by forming potentially malignant tumors or cancer cells. The dynamic interaction between these cells and their environment is crucial to the disease. Mathematical models can enhance our understanding of these interactions, helping us predict disease progression and treatment strategies. Methods In this study, we develop a fractional tumor-immune interaction model specifically for lung cancer (FTIIM-LC). We present some definitions and significant results related to the Caputo operator. We employ the generalized Laguerre polynomials (GLPs) method to find the optimal solution for the FTIIM-LC model. We then conduct a numerical simulation and compare the results of our method with other techniques and real-world data. Results We propose a FTIIM-LC model in this paper. The approximate solution for the proposed model is derived using a series of expansions in a new set of polynomials, the GLPs. To streamline the process, we integrate Lagrange multipliers, GLPs, and operational matrices of fractional and ordinary derivatives. We conduct a numerical simulation to study the effects of varying fractional orders and achieve the expected theoretical results. Conclusion The findings of this study demonstrate that the optimization methods used can effectively predict and analyze complex phenomena. This innovative approach can also be applied to other nonlinear differential equations, such as the fractional Klein–Gordon equation, fractional diffusion-wave equation, breast cancer model, and fractional optimal control problems.

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