Fractional-order dynamics in bacterial disease propagation: Modeling and analysis - Mahesh A. Yeolekar; Sagar R. Khirsariya; Jignesh P. Chauhan; Bijal M. Yeolekar (Franklin Open, 2025)
An analytical method to analyze a fractional-order bacterial disease model using the Caputo fractional derivative is developed in this paper. The system is solved using the Homotopy perturbation general transform method (HPGTM), giving approximate analytical solutions to the fractional-order model. To gain further insights into the dynamics of the disease, we derive the basic reproduction number R0 and examine the equilibria of the system to establish the conditions for local stability. Global stability of the equilibria is established by employing the Mittag-Leffler function method, which is particularly suitable for fractional-order systems. Numerical simulations provide examples of how varying fractional orders affect bacterial infection and recovery. Graphical results yield profound insights into the effect of bacterial infections, fractional-order dynamics, and control measures on the spread and eradication of the disease. The study serves as a basis for emphasizing the role of fractional calculus in modeling real-world biological systems and giving a full understanding of the behavior of bacterial diseases.