Mathematical analysis of scrub typhus seasonal infection with re-scaled transmission rate considering Northeast India reported data from 2010 to 2022

Healthcare reporting methods have seen a common problem with actual incidence of scrub typhus cases in Northeast India that were reported during post rainy season. We propose a Host-Vector model, a first of its kind, with a significant modification in the disease infection transmission rate. Our work aims to investigate a mathematical model by Atangana-Baleanu fractal-fractional operator that has seasonal pattern incorporating 2010-2022 data. The existence-uniqueness property is investigated using the fixed point theory, and also Ulam-Hyers stability is performed. Based on Lagrange's interpolation polynomial in the numerical scheme, a numerical investigation for various values of the fractional parameters is presented. The numerical simulation and phase plane trajectories demonstrates excellent performance of the suggested model as the number of individuals who recover rises gradually after herd immunity threshold points and turning points. Furthermore, the information gathered here may be useful for enhancing spatiotemporally dynamic scrub typhus disease models.