Comparative Analysis of Classical, Fractional, and Quantum Calculus Models for Measles Transmission Dynamics
- 1Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, Jordan
- 2Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan
- 3Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Abstract
This study presents three mathematical models of measles transmission that utilize pulse vaccination strategies: classical ordinary differential equations, Caputo fractional derivatives, and Jackson q-derivatives. The basic reproduction number R0 has been derived, and the global stability of equilibria has been investigated using an SIRS model with bilinear incidence. The quantum calculus model facilitates the integration of discrete-pulse vaccination strategies by applying geometric time scales. The existence, uniqueness, positivity, and global asymptotic stability of equilibria have been demonstrated through Lyapunov’s direct method. Numerical results indicate that while equilibria remain model-independent, transient dynamics exhibit significant variation. The fractional-derivative models reduce epidemic peaks by up to 5.6%, whereas the quantum-calculus model results in an increase of 1.1%. These models provide essential tools for enhancing pulse vaccination strategies in measles elimination initiatives.
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BibTeX
@article{darassi2026comparative,
title = {{Comparative Analysis of Classical, Fractional, and Quantum Calculus Models for Measles Transmission Dynamics}},
author = {Mahmoud H. DarAssi and Bashir Al-Hdaibat and Yousef AbuHour and Zuhur Alqahtani and Areej Almuneef},
journal = {Fractal and Fractional},
year = {2026},
month = oct,
doi = {10.3390/fractalfract10100692},
url = {https://www.mdpi.com/2504-3110/10/10/692},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Comparative Analysis of Classical, Fractional, and Quantum Calculus Models for Measles Transmission Dynamics
AU - Mahmoud H. DarAssi
AU - Bashir Al-Hdaibat
AU - Yousef AbuHour
AU - Zuhur Alqahtani
AU - Areej Almuneef
PY - 2026
DA - 2026/10/02
JO - Fractal and Fractional
DO - 10.3390/fractalfract10100692
UR - https://www.mdpi.com/2504-3110/10/10/692
AB - This study presents three mathematical models of measles transmission that utilize pulse vaccination strategies: classical ordinary differential equations, Caputo fractional derivatives, and Jackson q-derivatives. The basic reproduction number R0 has been derived, and the global stability of equilibria has been investigated using an SIRS model with bilinear incidence. The quantum calculus model facilitates the integration of discrete-pulse vaccination strategies by applying geometric time scales. The existence, uniqueness, positivity, and global asymptotic stability of equilibria have been demonstrated through Lyapunov’s direct method. Numerical results indicate that while equilibria remain model-independent, transient dynamics exhibit significant variation. The fractional-derivative models reduce epidemic peaks by up to 5.6%, whereas the quantum-calculus model results in an increase of 1.1%. These models provide essential tools for enhancing pulse vaccination strategies in measles elimination initiatives.
SN - 2504-3110
ER -