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Optimal control strategies of a fractional order model for Zika virus infection involving various transmissions

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  • Ali, Hegagi Mohamed
  • Ameen, Ismail Gad

Abstract

According to the world health organization (WHO), more than 17% of infectious diseases represented in vector-borne diseases (VBDs). So, more than 700,000 deaths annually caused by the spread of these diseases. Basically, VBDs are a usually used term that characterizes a disease transmitted to a host population, by vectors like mosquitoes, insects and ticks through feeding activity. Being a vector means that it carries a disease from an infective to a healthy host. In this paper, we address the fractional mathematical model which describes the transmission dynamics for one of the VBDs, that is Zika virus. We incorporated various combinations between four controls to reduce the transmission of this disease, the measures taken to reduce the contact among vectors and humans such as asleep under a bed net, wearing full clothes, stay in places with a screen window to keep the vector outside; the efforts to reduce the transmission rate from vectors to humans by increasing the autoimmunity; the efforts made to change sexual habits among a susceptible and infected human by using a condom at the period of Zika virus outbreak; and the measures taken to increase the death rate of vectors by using the insecticide spraying. The stability of all equilibrium points (EPs) of the fractional order model (FOM) is investigated. The control reproduction number Rc of the FOM is computed and the effect of the suggested controls on the behavior of Rc are presented graphically. Moreover, we characterized a fractional optimal control problem (FOCP) as well as used Pontryagin’s maximum principle to derive a fractional order necessary optimality conditions (NOCs). We solved these NOCs numerically by developing the forward-backward sweep method (FBSM) using the predictor-corrector method (PCM), where the state and adjoint equations in the form of the left Caputo fractional derivative (CFD). Furthermore, the outcomes are discussed with some figures and the approximate values for the cost functional are given based on the proposed strategies. Comparing all strategies with the uncontrolled case in order to choose the best strategy for reducing the spread of Zika virus infection.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002174
    DOI: 10.1016/j.chaos.2021.110864
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    References listed on IDEAS

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    1. L., Diego F. Aranda & González-Parra, Gilberto & Benincasa, Tommaso, 2019. "Mathematical modeling and numerical simulations of Zika in Colombia considering mutation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 1-18.
    2. 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).
    3. Ameen, I. & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2020. "An efficient algorithm for solving the fractional optimal control of SIRV epidemic model with a combination of vaccination and treatment," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    4. Karasu, Seçkin & Altan, Aytaç & Bekiros, Stelios & Ahmad, Wasim, 2020. "A new forecasting model with wrapper-based feature selection approach using multi-objective optimization technique for chaotic crude oil time series," Energy, Elsevier, vol. 212(C).
    5. I. Ameen & M. Hidan & Z. Mostefaoui & H.M. Ali, 2020. "Fractional Optimal Control with Fish Consumption to Prevent the Risk of Coronary Heart Disease," Complexity, Hindawi, vol. 2020, pages 1-13, February.
    6. Altan, Aytaç & Karasu, Seçkin & Bekiros, Stelios, 2019. "Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 325-336.
    7. Ebenezer Bonyah & Muhammad Altaf Khan & K O Okosun & Saeed Islam, 2017. "A theoretical model for Zika virus transmission," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-26, October.
    8. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    9. R. Rakkiyappan & V. Preethi Latha & Fathalla A. Rihan, 2019. "A Fractional-Order Model for Zika Virus Infection with Multiple Delays," Complexity, Hindawi, vol. 2019, pages 1-20, November.
    10. Srivastava, H.M. & Dubey, V.P. & Kumar, R. & Singh, J. & Kumar, D. & Baleanu, D., 2020. "An efficient computational approach for a fractional-order biological population model with carrying capacity," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    11. Ali, Hegagi Mohamed & Ameen, Ismail Gad, 2020. "Save the pine forests of wilt disease using a fractional optimal control strategy," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    12. Sweilam, N.H. & AL-Mekhlafi, S.M. & Alshomrani, A.S. & Baleanu, D., 2020. "Comparative study for optimal control nonlinear variable-order fractional tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    13. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Olivares, Alberto & Staffetti, Ernesto, 2023. "A statistical moment-based spectral approach to the chance-constrained stochastic optimal control of epidemic models," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Ameen, Ismail Gad & Baleanu, Dumitru & Ali, Hegagi Mohamed, 2022. "Different strategies to confront maize streak disease based on fractional optimal control formulation," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Sharma, Naveen & Singh, Ram & Singh, Jagdev & Castillo, Oscar, 2021. "Modeling assumptions, optimal control strategies and mitigation through vaccination to Zika virus," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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