Advanced Mathematical Models & Applications

In this study, we proposes a novel fractional-order SEI-C-SAEITR model to examine the transmission dynamics of the Seoul virus from rodent reservoirs to humans through direct and indirect routes. The proposed model is formulated in terms of a fractal–fractional differential operator in the Caputo sense with a power-law kernel, defined by the fractional order χ and the fractal dimension η. By applying the fractal-fractional operator, we have demonstrated both the existence and uniqueness of solutions for the proposed model using the Banach fixed-point theorem along with Leray-Schauder’s approach. The disease-free and endemic equilibrium points are calculated to examine the conditions for virus eradication and persistence. It is proved that the basic reproduction number R₀ serves as a threshold parameter that the infection decreases when R₀ < 1 and persists when R₀ > 1. Approximate analytical solutions are obtained using the Laplace–Adomian Decomposition Method (LADM). The model's behavior under a variety of parameter values is tested using numerical simulations for a range of fractional orders and fractal dimensions. The results illustrate that the fractal–fractional operator produces more accurate and realistic dynamics than classical integer-order models. Graphical presentations identify the impact of fractional parameters on the spread and control of disease.