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Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order

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  • Nasser Hassan Sweilam
  • Seham Mahyoub Al-Mekhlafi
  • Taghreed Abdul Rahman Assiri

Abstract

A novel mathematical fractional model of multistrain tuberculosis with time delay memory is presented. The proposed model is governed by a system of fractional delay differential equations, where the fractional derivative is defined in the sense of the Grünwald–Letinkov definition. Modified parameters are introduced to account for the fractional order. The stability of the equilibrium points is investigated for any time delay. Nonstandard finite deference method is proposed to solve the resulting system of fractional-order delay differential equations. Numerical simulations show that nonstandard finite difference method can be applied to solve such fractional delay differential equations simply and effectively.

Suggested Citation

  • Nasser Hassan Sweilam & Seham Mahyoub Al-Mekhlafi & Taghreed Abdul Rahman Assiri, 2017. "Numerical Study for Time Delay Multistrain Tuberculosis Model of Fractional Order," Complexity, Hindawi, vol. 2017, pages 1-14, July.
    • Handle: RePEc:hin:complx:1047384
    DOI: 10.1155/2017/1047384
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    References listed on IDEAS

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    3. Arenas, Abraham J. & González-Parra, Gilberto & Chen-Charpentier, Benito M., 2016. "Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 121(C), pages 48-63.
    4. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
    5. Anguelov, Roumen & Lubuma, Jean M.-S., 2003. "Nonstandard finite difference method by nonlocal approximation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(3), pages 465-475.
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