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Dynamics Of Visceral Leishmania Epidemic Model With Non-Singular Kernel

Author

Listed:
  • YI ZHAO

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, P. R. China)

  • AMIR KHAN

    (Department of Mathematics, Faculty of Science, King Mongkuts, University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • USA WANNASINGHA HUMPHRIES

    (Department of Mathematics, Faculty of Science, King Mongkuts, University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • RAHAT ZARIN

    (Department of Basic Sciences, University of Engineering and Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan)

  • MAJID KHAN

    (Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan)

  • ABDULLAHI YUSUF

    (Department of Computer Engineering, Biruni University, Istanbul, Turkey6Department of Mathematics, Near East University, TRNC, Mersin 10, Turkey)

Abstract

In this paper, we have taken into consideration the most dangerous form of leishmaniasis known as visceral leishmaniasis, which has the highest fatality rate and is also famous with the name of kala-azar. The analysis is carried out using Atangana–Baleanu–Caputo (ABC) operator with a convex incidence rate. Using fixed point theorems the existence and uniqueness for the solutions of the fractional leishmania epidemic model have been established. All the basic properties of the given model are studied along with stability analysis. Newton polynomial and Adams–Bashforth methods are taken into account to find the numerical solution.

Suggested Citation

  • Yi Zhao & Amir Khan & Usa Wannasingha Humphries & Rahat Zarin & Majid Khan & Abdullahi Yusuf, 2022. "Dynamics Of Visceral Leishmania Epidemic Model With Non-Singular Kernel," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-27, August.
    • Handle: RePEc:wsi:fracta:v:30:y:2022:i:05:n:s0218348x22401351
    DOI: 10.1142/S0218348X22401351
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