New Preprint Alert
This work represents a true cross-border scientific partnership combining expertise from: Yemen (Sana'a University), Algeria (University of Adrar) and Germany (University of Wuppertal).
Epidemic modeling helps us understand and control the spread of infectious diseases. However, traditional integer-order models struggle to capture the complex memory and hereditary effects inherent to biological processes. To overcome this, we propose a novel fractional-order SVIR (Susceptible-Vaccinated-Infected-Recovered) epidemic model utilizing a breakthrough hybrid Mittag-Leffler-Caputo-Fabrizio (MLCF) operator with a non-singular kernel.
The Key Highlights & Innovations:
- Dual Memory Capture: The hybrid MLCF operator successfully captures both short- and long-term memory effects within a unified, non-singular framework.
- Mathematical Rigor: We comprehensively investigate the basic reproduction number ($\mathcal{R}_{0}$), local/global stability properties, and prove the positivity and boundedness of the solutions.
- Advanced Numerical Framework: We developed a customized $\theta$-weighted Nonstandard Finite Difference (NSFD) method. This advanced numerical scheme preserves the essential qualitative properties of the continuous model (like positivity and boundedness) and guarantees unconditional stability.
- Insightful Analyses: Through sensitivity and bifurcation analyses, we demonstrate exactly how fractional memory parameters influence the real-time evolution of an epidemic.
Read the full preprint here: (PDF) Structure-Preserving Schemes for a Fractional SVIR Epidemic Model with a Hybrid Mittag-Leffler-Caputo-Fabrizio Operator
