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A fractional order SIR epidemic model for dengue transmission

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  • Hamdan, Nur ’Izzati
  • Kilicman, Adem

Abstract

In the present work, we study the fractional order differential equation of the dengue epidemic system based on the susceptible-infected-recuperated (SIR) model. The threshold quantity value R0 similar to the basic reproduction number is obtained using the next-generation matrix approach. The local stability of the disease-free equilibrium (DFE) point and endemic equilibrium point is presented. Using the linearization theorem, we achieved that DFE is locally asymptotically stable when R0 < 1 and is unstable when R0 > 1. When R0 > 1, the endemic equilibrium is locally asymptotically stable. Numerical simulations are given for different parameter setting of the order of derivative α. The proposed model is validated using published weekly dengue cases in Malaysia which were recorded in 2016. It is observed that the proposed model provides a more realistic way to understand the dynamic of dengue disease.

Suggested Citation

  • Hamdan, Nur ’Izzati & Kilicman, Adem, 2018. "A fractional order SIR epidemic model for dengue transmission," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 55-62.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:55-62
    DOI: 10.1016/j.chaos.2018.06.031
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    References listed on IDEAS

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    1. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
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    Cited by:

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    2. Yadav, Ram Prasad & Renu Verma,, 2020. "A numerical simulation of fractional order mathematical modeling of COVID-19 disease in case of Wuhan China," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Malik, Hafiz Abid Mahmood & Abid, Faiza & Wahiddin, Mohamed Ridza & Waqas, Ahmad, 2021. "Modeling of internal and external factors affecting a complex dengue network," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Tuan Hoang, Manh & Nagy, A.M., 2019. "Uniform asymptotic stability of a Logistic model with feedback control of fractional order and nonstandard finite difference schemes," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 24-34.
    5. Zhou, Jiaying & Ye, Yong & Arenas, Alex & Gómez, Sergio & Zhao, Yi, 2023. "Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    6. Wang, Yupin & Liu, Shutang & Li, Hui & Wang, Da, 2019. "On the spatial Julia set generated by fractional Lotka-Volterra system with noise," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 129-138.
    7. Soudeep Deb & Sougata Deb, 2022. "An ensemble method for early prediction of dengue outbreak," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(1), pages 84-101, January.
    8. Agus Suryanto & Isnani Darti & Hasan S. Panigoro & Adem Kilicman, 2019. "A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting," Mathematics, MDPI, vol. 7(11), pages 1-13, November.

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