Fractional epidemic modeling of dengue: Sensitivity, stability, and bifurcation under environmental influence

Razia Sultana; Md Rifat Hasan; Turki D. Alharbi; J. G. AL-Juaid; M. T. Alharthi; Razia Sultana; Md Rifat Hasan; Turki D. Alharbi; J. G. AL-Juaid; M. T. Alharthi

doi:10.3934/math.2026842

AIMS Mathematics

2026, Volume 11, Issue 7: 20711-20745. doi: 10.3934/math.2026842

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Fractional epidemic modeling of dengue: Sensitivity, stability, and bifurcation under environmental influence

1.
Department of Applied Mathematics, Faculty of Science, Noakhali Science and Technology University, Noakhali 3814, Bangladesh; raziasultana0081@gmail.com; rifatmathdu@gmail.com
2.
Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 24381, Saudi Arabia; tdharbi@uqu.edu.sa
3.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia; jo.gh@tu.edu.sa
4.
Department of Mathematics, Applied College at Khulais, University of Jeddah, Jeddah 21589, Saudi Arabia; mtalharthi@uj.edu.sa

Received: 04 May 2026 Revised: 20 June 2026 Accepted: 29 June 2026 Published: 14 July 2026
MSC : 34A08, 34D20, 34C60, 37G10, 92D30

Dengue fever is a rapidly spreading vector-borne disease, posing severe health challenges worldwide due to its complex transmission dynamics between humans and mosquitoes. Traditional mathematical models often fail to capture memory effects and environmental influences that significantly affect disease progression. To address this, we formulated a fractional-order dengue transmission model incorporating environmental factors using the Caputo derivative. This approach allows the system dynamics to account for hereditary effects and delayed responses, providing a more realistic representation of dengue outbreaks. We analyzed the model's stability, bifurcation, and sensitivity, and conducted numerical simulations to examine how varying the fractional order and key epidemiological parameters impacts the disease dynamics. Our findings show that lower fractional orders slow the epidemic's progression, while higher orders approach classical integer-order behavior. The mosquito biting rate emerged as the most influential factor affecting the basic reproduction ($ R_0 $), whereas disease-induced human mortality had minimal impact. These results highlight critical parameters for controlling dengue's transmission and demonstrate that fractional-order models offer enhanced predictive power and insight compared with traditional models, supporting more effective public health interventions.
- dengue,
- fractional differential equation,
- bifurcation,
- Lyapunov,
- environment,
- sensitivity,
- stability
Citation: Razia Sultana, Md Rifat Hasan, Turki D. Alharbi, J. G. AL-Juaid, M. T. Alharthi. Fractional epidemic modeling of dengue: Sensitivity, stability, and bifurcation under environmental influence[J]. AIMS Mathematics, 2026, 11(7): 20711-20745. doi: 10.3934/math.2026842

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Abstract

Dengue fever is a rapidly spreading vector-borne disease, posing severe health challenges worldwide due to its complex transmission dynamics between humans and mosquitoes. Traditional mathematical models often fail to capture memory effects and environmental influences that significantly affect disease progression. To address this, we formulated a fractional-order dengue transmission model incorporating environmental factors using the Caputo derivative. This approach allows the system dynamics to account for hereditary effects and delayed responses, providing a more realistic representation of dengue outbreaks. We analyzed the model's stability, bifurcation, and sensitivity, and conducted numerical simulations to examine how varying the fractional order and key epidemiological parameters impacts the disease dynamics. Our findings show that lower fractional orders slow the epidemic's progression, while higher orders approach classical integer-order behavior. The mosquito biting rate emerged as the most influential factor affecting the basic reproduction ($ R_0 $), whereas disease-induced human mortality had minimal impact. These results highlight critical parameters for controlling dengue's transmission and demonstrate that fractional-order models offer enhanced predictive power and insight compared with traditional models, supporting more effective public health interventions.

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