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Modeling the dynamics of Hepatitis E with optimal control

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  • Alzahrani, E.O.
  • Khan, M.A.

Abstract

The present paper shows the dynamics of Hepatitis E with optimal control. The paper is analyzed by two different aspects: first, we explore the dynamics of Hepatitis E model and then applying the optimal control analysis. Secondly, we use the most appropriate and recent fractional order derivative called the Atangana–Baleanu derivative for the dynamical analysis of Hepatitis E model. The proposed model considered is locally asymptotically stable when the threshold quantity less than one. Further, we explore the stability analysis of the model when R0>1. Then, we choose some appropriate control to formulate the optimality system. The results associated to the optimal control are obtained and discussed with different strategies. Moreover, we apply Atangana–Baleanu derivative to the proposed model and obtain the required results necessary for the fractional order model. Numerical results for the optimal control problem and Atangana–Baleanu derivative are obtained and discussed in detail. The results suggest that control variables chosen should be properly applied to get rid of the infection of Hepatitis E. The Atangana–Baleanu derivative results suggest that at any time t we can check the disease status and make a useful strategy for the early elimination of Hepatitis E from the community.

Suggested Citation

  • Alzahrani, E.O. & Khan, M.A., 2018. "Modeling the dynamics of Hepatitis E with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 287-301.
    • Handle: RePEc:eee:chsofr:v:116:y:2018:i:c:p:287-301
    DOI: 10.1016/j.chaos.2018.09.033
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    References listed on IDEAS

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    1. Khan, Muhammad Altaf & Islam, Saeed & Zaman, Gul, 2018. "Media coverage campaign in Hepatitis B transmission model," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 378-393.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    4. Khan, Muhammad Altaf & Khan, Rizwan & Khan, Yasir & Islam, Saeed, 2018. "A mathematical analysis of Pine Wilt disease with variable population size and optimal control strategies," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 205-217.
    5. Atangana, Abdon & Gómez-Aguilar, J.F., 2018. "Fractional derivatives with no-index law property: Application to chaos and statistics," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 516-535.
    6. Khan, Muhammad Altaf & Khan, Yasir & Islam, Saeed, 2018. "Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 210-227.
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    Cited by:

    1. Nisar, Kottakkaran Sooppy & Logeswari, K. & Ravichandran, C. & Sabarinathan, S., 2023. "New frame of fractional neutral ABC-derivative with IBC and mixed delay," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Liu, Yujiang & Gao, Shujing & Liao, Zhenzhen & Chen, Di, 2022. "Dynamical behavior of a stage-structured Huanglongbing model with time delays and optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Kolebaje, Olusola & Popoola, Oyebola & Khan, Muhammad Altaf & Oyewande, Oluwole, 2020. "An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).

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