Modeling Dengue Dynamics Using Classical, Caputo Fractional, and Fractal Derivatives (European Journal of Pure and Applied Mathematics, 2025)
Dengue is a major problem in Sudan. Dengue spreads in Gedaref, Sudan. In this work, we compare classical, Caputo fractional derivative, and fractal SIAR-SI pandemic models. We investigate the disease-free and endemic equilibrium stability, two important stable states of the proposed dynamical model. This study identifies the factors guiding a disease’s persistence or  extinction in the population. The model is fitted using real data from Gedaref, Sudan, and the Markov Chain Monte Carlo method is used for estimating parameters. The computed R0 = 3.27, indicating that the disease is endemic. The classical model fits the real data better than the other methods. The fractional model, involving Caputo derivatives, explains memory effects. Thus, they provide a more realistic formulation of disease transmission. The fractal model with Hausdorff derivatives offers a new direction for complicated transmission dynamics and is worthy of further research. The fractional and fractal models outperform the classical model by treating long-term dependency with fractional derivatives and disease spread accurately with fractal operators.
Keywords: Dengue fever, mathematical modeling, fractional derivatives, fractals, epidemiology, forecasting.