Modeling Seoul Virus Transmission Dynamics through Fractal-Fractional Derivatives and Laplace-Adomian Decomposition

In this study, a novel fractional-order SEI-C-SAEITR model is proposed 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 and the fractal dimension .Both the existence and uniqueness of solutions is demonstrated by applying the fractal-fractional operator 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.Furthermore, performs a sensitivity analysis to identify key parameters that significantly influence the basic reproduction number.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.