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Analysis of a nonlinear fractional system for Zika virus dynamics with sexual transmission route under generalized Caputo-type derivative

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Abstract

This paper establishes a mathematical model of the Zika virus infection with the sexual transmission route under the generalized Caputo-type fractional derivative. The model consists of a system of eleven nonlinear fractional differential equations. The existence and uniqueness results are derived by applying Banach’s and Schaüder’s fixed point theorems. The different types of Ulam’s stability results for the fractional model are examined. The corrector-predictor algorithm has been applied to illustrate the approximated solutions and analyze the dynamical behavior of the fractional model under consideration. In addition, various numerical simulations are presented corresponding to different fractional-orders in \(\alpha \in [0,1]\).

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Acknowledgements

The fifth and sixth authors were supported by Azarbaijan Shahid Madani University. The authors express their gratitude to dear unknown referees for their helpful suggestions which improved the final version of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Burapha University, Chonburi, 20131, Thailand

    Chatthai Thaiprayoon & Jutarat Kongson

  2. Center of Excellence in Mathematics, CHE, Sri Ayutthaya Rd., Bangkok, 10400, Thailand

    Chatthai Thaiprayoon & Jutarat Kongson

  3. Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Weerawat Sudsutad

  4. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

    Jehad Alzabut

  5. Group of Mathematics, Faculty of Engineering, Ostim Technical University, Ankara, 06374, Turkey

    Jehad Alzabut

  6. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran

    Sina Etemad & Shahram Rezapour

  7. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

    Shahram Rezapour

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Thaiprayoon, C., Kongson, J., Sudsutad, W. et al. Analysis of a nonlinear fractional system for Zika virus dynamics with sexual transmission route under generalized Caputo-type derivative. J. Appl. Math. Comput. 68, 4273–4303 (2022). https://doi.org/10.1007/s12190-021-01663-1

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  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-021-01663-1

Keywords

Mathematics Subject Classification