A novel fractional-order model with data-driven validation for the dynamics of complex epidemic spreading in networks
Mahmoud Rokaya , Dalia I. Hemdan , Mohammed A. Alzain , El-Sayed Atlam
An International Journal of Optimization and Control: Theories & Applications ›› 2026, Vol. 16 ›› Issue (1) : 111 -137.
Mathematical modeling of epidemics is a cornerstone in the study and response to the spread of diseases and related processes across various domains. However, classical models generally do not describe such memory effects properly and are computationally inefficient, which restricts their applicability or predictive accuracy. To address these issues, we introduce a new approach to epidemic modeling using our newly proposed fractional-order differential equations, which are endowed with the Atangana–Baleanu system to describe long-range dependencies and nonlinear characteristics more accurately than the traditional Caputo system. To address this, we develop physics-informed neural networks and Fourier-based artificial intelligence-driven surrogate solvers, which are computationally efficient without compromising accuracy. To actuate intervention policies in a dynamic fashion, we also incorporate a hybrid control mechanism integrating the use of reinforcement learning with classical mathematical optimization to facilitate adaptive policymaking that benefits from data. Unlike existing work, our framework is rigorously evaluated on real-world epidemiological datasets from the World Health Organization and the Centers for Disease Control and Prevention, and tested extensively for out-of-the-box adaptability to cybersecurity (cyber malware), social rumor, and financial contagion problems. We also propose a data-free generative model (Fair4Free) that improves fairness, privacy, and utility in synthetic dataset generation, allowing its use even for constrained-data settings. Experimental evidence indicates that our holistic approach enhances the accuracy of predictive performance compared to baselines, with both lower computational cost and cross-domain generalizability to unprecedented settings. Finally, we set a new state-of-the-art for EpiModel by end-to-end training on fair data.
Fractional calculus / Epidemic modeling / Physics-informed neural networks / Reinforcement learning / Optimal control / Real-world validation / Data fairness
| [1] |
|
| [2] |
|
| [3] |
|
| [4] |
|
| [5] |
|
| [6] |
|
| [7] |
|
| [8] |
|
| [9] |
|
| [10] |
|
| [11] |
|
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
|
| [16] |
|
| [17] |
|
| [18] |
|
| [19] |
|
| [20] |
|
| [21] |
|
| [22] |
|
| [23] |
|
| [24] |
|
| [25] |
|
| [26] |
|
| [27] |
|
| [28] |
|
| [29] |
|
| [30] |
|
| [31] |
|
| [32] |
|
| [33] |
|
| [34] |
|
| [35] |
|
| [36] |
|
| [37] |
|
| [38] |
|
| [39] |
|
| [40] |
|
| [41] |
|
/
| 〈 |
|
〉 |
PDF
(12896KB)
