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Fractional modeling for the spread of Hookworm infection under Caputo operator

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  • Mustapha, Umar Tasiu
  • Qureshi, Sania
  • Yusuf, Abdullahi
  • Hincal, Evren

Abstract

It is estimated that, about one billion people mostly from Asia, Sub-Saharan Africa and Latin America are infected with the Hookworm infection. In this paper, we developed and analyzed a model for the transmission dynamics of Hookworm infection in a human population using Caputo fractional order differential operator. Under Caputo operator, existence and uniqueness for the solutions of the new Hookworm infection model have been analyzed using fixed point theorems. Parameters of the model are estimated with the help of real statistics available for the Hookworm infection from a city of Ghana and the best fit is obtained under the nonlinear least-squares curve fitting technique. Further analysis of the proposed model shows that the disease free (infection-absent) equilibrium is locally asymptotically stable whenever a certain reproduction number R0<1 and the endemic (infection-present) equilibrium point is globally asymptotically stable whenever R0<1 and unstable if R0>1. Using forward normalized sensitivity index, the most sensitive parameters are identified that are essential for control of the infection and we obtained different types of simulations for the proposed Hookworm transmission system with the best fitted fractional order parameter (χ). The modelling results show that the chemotherapy treatment, awareness and improvement of personal hygiene are the best measures to be taken for control of the Hookworm infection among vulnerable community.

Suggested Citation

  • Mustapha, Umar Tasiu & Qureshi, Sania & Yusuf, Abdullahi & Hincal, Evren, 2020. "Fractional modeling for the spread of Hookworm infection under Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302782
    DOI: 10.1016/j.chaos.2020.109878
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    References listed on IDEAS

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    1. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Modeling chickenpox disease with fractional derivatives: From caputo to atangana-baleanu," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 111-118.
    2. Jajarmi, Amin & Arshad, Sadia & Baleanu, Dumitru, 2019. "A new fractional modelling and control strategy for the outbreak of dengue fever," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. Hajipour, Mojtaba & Jajarmi, Amin & Malek, Alaeddin & Baleanu, Dumitru, 2018. "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 146-158.
    4. Qureshi, Sania & Yusuf, Abdullahi & Shaikh, Asif Ali & Inc, Mustafa, 2019. "Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    5. Qureshi, Sania & Yusuf, Abdullahi, 2019. "Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 32-40.
    6. Wang, Wanting & Khan, Muhammad Altaf & Fatmawati, & Kumam, P. & Thounthong, P., 2019. "A comparison study of bank data in fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 369-384.
    7. Qureshi, Sania & Atangana, Abdon, 2019. "Mathematical analysis of dengue fever outbreak by novel fractional operators with field data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    8. 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.
    9. Qureshi, Sania & Bonyah, Ebenezer & Shaikh, Asif Ali, 2019. "Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
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    Cited by:

    1. Kumar, Sunil & Chauhan, R.P. & Momani, Shaher & Hadid, Samir, 2021. "A study of fractional TB model due to mycobacterium tuberculosis bacteria," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Yusuf, Abdullahi & Tasiu Mustapha, Umar & Abdulkadir Sulaiman, Tukur & Hincal, Evren & Bayram, Mustafa, 2021. "Modeling the effect of horizontal and vertical transmissions of HIV infection with Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Kuddus, Md Abdul & McBryde, Emma S. & Adekunle, Adeshina I. & White, Lisa J. & Meehan, Michael T., 2021. "Mathematical analysis of a two-strain disease model with amplification," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Acay, Bahar & Inc, Mustafa & Mustapha, Umar Tasiu & Yusuf, Abdullahi, 2021. "Fractional dynamics and analysis for a lana fever infectious ailment with Caputo operator," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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