Novel tick-borne encephalitis transmission dynamics: A model-based strategy for epidemic control

This study, we present a fractional-order compartmental model to describe the transmission dynamics of tick-borne encephalitis between human and vector (tick) populations. The model is first formulated in the classical integer-order sense and then extended to a fractional-order framework using the Caputo fractional derivative to incorporate memory effects. We analyzed the model with respect to positivity, boundedness, and stability, and identified the invariant region under the Caputo fractional operator. Furthermore, the model was fitted to the reported case data, and $ \mathcal{R}_0 $ was computed using the next-generation matrix method, resulting in $ \mathcal{R}_0 = 0.23 $. PRCC sensitivity analysis confirmed the effectiveness of vaccination in reducing disease transmission, with local and global stability established through Jacobian and Lyapunov analyses, respectively. We examined the effect of the fractional-order parameter $ \zeta $ using an efficient Adams-Moulton numerical approach, and contour and 3D surface plots are used to visualize the outcomes. The simulations showed that variations in key parameters reduced disease transmission and infection levels in both populations.