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Fractional Mathematical Modelling of Malaria Disease with Treatment & Insecticides

PUBLISHED October 05, 2022 (DOI: https://doi.org/10.54985/peeref.2210p3573404)



Muhammad Sinan1 , Hijaz Ahmad2 , Zubair Ahmad3 , Jamel Baili4 , Saqib Murtaza5 , M.A. Aiyashi6 , Thongchai Botmart7
  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, China
  2. Information Technology Application and Research Center, Istanbul Ticaret University, 34445, Istanbul
  3. Dipartimento di Matematica e Fisica, Università degli Studi della Campania “Luigi Vanvitelli”
  4. College of Computer Science, King Khalid University, Abha 61413, Saudi Arabia
  5. Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Thailand
  6. Department of Mathematics, Faculty of Science, Jazan University, Saudi Arabia
  7. Department of MathematicsFaculty of Science, Khon Kaen University, Thailand

Conference / event

Mathematical Modelling of Infectious Diseases, September 2022 (Virtual)

Poster summary

The dynamics of malaria illness among humans and vectors are examined in this study. The problem is described using nonlinear ODEs that are then generalized using the Atangana-Baleanu fractional derivative. Optimal control strategies have been done. From the graphical results, it can be noticed that the control parameters drastically decrease the number of infected human and vector population which will off course minimize the spread of infection among the human population. Moreover, the use of bednets and insecticides can reduce the spread of infection dramatically while the impact of medication and treatment on the control of infection is comparatively less.


Atangana baleanu operator, Mittag-Leffler function, Existence and uniqueness, Ulam stability analysis, Mathematical modeling, Optimal control strategies

Research areas



  1. Dumitru Baleanu and Babak Shiri. Numerical methods for solving systems of atangana-baleanu fractional differential equations. In Applications of Fractional Calculus to Modeling in Dynamics and Chaos, pages 353–378. Chapman and Hall/CRC
  2. Muhammad Sinan, Hijaz Ahmad, Zubair Ahmad, Jamel Baili, Saqib Murtaza, MA Aiyashi, and Thongchai Botmart. Fractional mathematical modeling of malaria disease with treatment & insecticides. Results in Physics, 34:105220, 2022.
  3. Muhammad Sinan, Kamal Shah, Poom Kumam, Ibrahim Mahariq, Khursheed J Ansari, Zubair Ahmad, and Zahir Shah. Fractional order mathematical modeling of typhoid fever disease. Results in Physics, 32:105044, 2022.


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Additional information

Competing interests
No competing interests were disclosed.
Data availability statement
Data sharing not applicable to this poster as no datasets were generated or analyzed during the current study.
Creative Commons license
Copyright © 2022 Sinan et al. This is an open access work distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Sinan, M., Ahmad, H., Ahmad, Z., Baili, J., Murtaza, S., Aiyashi, M., Botmart, T. Fractional Mathematical Modelling of Malaria Disease with Treatment & Insecticides [not peer reviewed]. Peeref 2022 (poster).
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