Dynamics and control of a fractional fractal Mittag-Leffler SV EI1I2R model for Lumpy skin disease
DOI:
https://doi.org/10.48165/jmmfc.2026.3101Keywords:
Fractional fractal Mittag-Leffler, SEVIR model, Hopf bifurcation, Sensitivity analysis, Optimal control, Epidemic dynamicsAbstract
In this Study we extend the work of Reem K. Alhefthi [12] on Lumpy Skin Disease (LSD) dynam ics using symptomatic and asymptomatic measures with a Mittag-Leffler kernel, we propose a fractional fractal Mittag-Leffler SV EI1I2R model to capture memory and hereditary effects in disease transmission. The mod elŠs dynamical behavior is rigorously analyzed, including local and global stability and the basic reproduction number. We derive conditions for Hopf bifurcation, revealing scenarios that may trigger oscillatory outbreaks. A detailed sensitivity analysis identifies critical epidemiological and control parameters that significantly influ ence disease spread. Additionally, an optimal control framework based on PontryaginŠs Maximum Principle is developed to minimize infection via vaccination, treatment, and isolation strategies. Numerical simulations demonstrate the profound impact of fractional-order dynamics on epidemic progression, offering insights into the interaction between bifurcation phenomena, parameter sensitivities, and optimal interventions. This study provides a robust, integrated framework for understanding, predicting, and controlling LSD in livestock popula tions.
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