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<p>Malaria, a vector-borne disease transmitted by female Anopheles mosquitoes, a lethal insect instigator, is typically found in tropical and subtropical locations. In this paper, we developed the new malaria disease fractional order model under the Mittag-Leffler kernel to understand the dynamics and preventive control of malaria transmission in Northern Cyprus. The model is formulated as a deterministic eight-compartmental with subpopulations of humans and mosquitos for this study. The qualitative study of the suggested model is thoroughly presented, including an outline of its essential properties and a review of theorems. Linear growth and Lipschitz criteria are used to verify the existence and uniqueness of solutions. Along with determining the equilibrium points and reproductive number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((R_0)\)</EquationSource> </InlineEquation> for sensitivity analysis of the system with sensitivity index parameters. The malaria fractional order model was analyzed as locally asymptotically stable, and the Lyapunov function first derivative test for global stability. The Newton Polynomial method is used to generate the algorithm for numerical simulations at different fractal order values and fractal dimensions to understand the impact of infection dynamics in the region that support theoretical results. The asymptotically stable worldwide endemic equilibrium revealed by numerical simulations highlights the necessity of major efforts to reduce malaria. The findings indicate a considerable rise in susceptible human populations and a decline in infectious mosquito numbers. It could be worthwhile to consider making a few significant adjustments to the current methodology in future studies.</p>

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Fractal fractional approach to investigate the forecasting and dynamics of malaria disease for early control precaution

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  • 出版模式：

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  • 发表日期：

    2025年12月1日

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  • Muhammad Farman,
  • Ulas Hurdoganoglu,
  • Nehir Hincal,
  • Nezihal Gokbulut,
  • Emrah Guler,
  • Kaya Suer,
  • Aceng Sambas,
  • Evren Hincal

摘要

Malaria, a vector-borne disease transmitted by female Anopheles mosquitoes, a lethal insect instigator, is typically found in tropical and subtropical locations. In this paper, we developed the new malaria disease fractional order model under the Mittag-Leffler kernel to understand the dynamics and preventive control of malaria transmission in Northern Cyprus. The model is formulated as a deterministic eight-compartmental with subpopulations of humans and mosquitos for this study. The qualitative study of the suggested model is thoroughly presented, including an outline of its essential properties and a review of theorems. Linear growth and Lipschitz criteria are used to verify the existence and uniqueness of solutions. Along with determining the equilibrium points and reproductive number \((R_0)\) for sensitivity analysis of the system with sensitivity index parameters. The malaria fractional order model was analyzed as locally asymptotically stable, and the Lyapunov function first derivative test for global stability. The Newton Polynomial method is used to generate the algorithm for numerical simulations at different fractal order values and fractal dimensions to understand the impact of infection dynamics in the region that support theoretical results. The asymptotically stable worldwide endemic equilibrium revealed by numerical simulations highlights the necessity of major efforts to reduce malaria. The findings indicate a considerable rise in susceptible human populations and a decline in infectious mosquito numbers. It could be worthwhile to consider making a few significant adjustments to the current methodology in future studies.