Abstract
This study investigates the complex transmission dynamics of malaria, a critical global health challenge, with a focus on the African continent. We introduce a novel approach that employs Fractional Differential Equations (FDEs) to advance the understanding of malaria spread and control. Specifically, we develop a new SIR-SI model using the Caputo fractional operator, which captures the memory effects and time-delay characteristics inherent in real-world epidemiological systems. A detailed analysis of the model's solvability and uniqueness is conducted using fixed-point theory. To obtain an analytical solution, the system is solved via the Laplace transform method, with solutions expressed in closed form using the Mittag-Leffler function. The model accounts for the non-local nature of disease spread, underscoring the significant influence of past disease states on current transmission dynamics. Furthermore, we present a modified governing model, analyze its stability and convergence, and employ an efficient iterative Grünwald-Letnikov (GL) method for numerical solution. Simulations demonstrate the impact of key parameters on disease dynamics. The results indicate that the fractional-order model offers a more accurate and comprehensive representation of malaria.
Recommended Citation
Farah, Gassan A. M. O.; Mukhtar, Abdulaziz Y. A.; and Patidar, Kailash C.
(2025)
"Mathematical analysis and numerical simulation of a fractional-order SIR-SI model for malaria transmission dynamics,"
Mathematical Modelling and Numerical Simulation with Applications: Vol. 5:
Iss.
4, Article 2.
DOI: https://doi.org/10.53391/2791-8564.1010
Available at:
https://mmnsa.researchcommons.org/journal/vol5/iss4/2
Included in
Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Virus Diseases Commons