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Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission

Author

Listed:
  • Iqbal, Zafar
  • Ahmed, Nauman
  • Baleanu, Dumitru
  • Adel, Waleed
  • Rafiq, Muhammad
  • Aziz-ur Rehman, Muhammad
  • Alshomrani, Ali Saleh

Abstract

In this article, an integer order nonlinear HIV/AIDS infection model is extended to the non-integer nonlinear model. The Grunwald Letnikov nonstandard finite difference scheme is designed to obtain the numerical solutions. Structure preservence is one of the main advantages of this scheme. Reproductive number R0 is worked out and its key role in disease dynamics and stability of the system is investigated with the following facts, if R0 < 1 the disease will be diminished and it will persist in the community for R0 > 1. On the other hand, it is sought out that system is stable when R0 < 1 and R0 > 1 implicates that system is locally asymptotically stable. Positivity and boundedness of the scheme is also proved for the generalized system. Two steady states of the system are computed and verified by computer simulations with the help of some suitable test problem.

Suggested Citation

  • Iqbal, Zafar & Ahmed, Nauman & Baleanu, Dumitru & Adel, Waleed & Rafiq, Muhammad & Aziz-ur Rehman, Muhammad & Alshomrani, Ali Saleh, 2020. "Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301089
    DOI: 10.1016/j.chaos.2020.109706
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    References listed on IDEAS

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    1. Moghadas, S.M. & Gumel, A.B., 2002. "Global stability of a two-stage epidemic model with generalized non-linear incidence," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 60(1), pages 107-118.
    2. 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.
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    Cited by:

    1. Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Mohammad Izadi & Mahmood Parsamanesh & Waleed Adel, 2022. "Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System," Mathematics, MDPI, vol. 10(23), pages 1-26, December.
    3. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2021. "Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Sweilam, N.H. & AL - Mekhlafi, S.M. & Mohamed, D.G., 2021. "Novel chaotic systems with fractional differential operators: Numerical approaches," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Goyal, Manish & Baskonus, Haci Mehmet & Prakash, Amit, 2020. "Regarding new positive, bounded and convergent numerical solution of nonlinear time fractional HIV/AIDS transmission model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Brian Villegas-Villalpando & Jorge E. Macías-Díaz & Qin Sheng, 2022. "Solution Spaces Associated to Continuous or Numerical Models for Which Integrable Functions Are Bounded," Mathematics, MDPI, vol. 10(11), pages 1-6, June.

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