Caputo fractional-order SVIR model for rotavirus: Numerical solutions using Laplace-Adomian decomposition method

Rotavirus is a leading cause of severe gastroenteritis and diarrheal mortality in children under five years of age, especially in developing countries. Mathematical modeling plays a crucial role in understanding the transmission dynamics of rotavirus and in evaluating the impact of vaccination strategies. In this study, a Caputo fractional-order susceptible-vaccinated-infected-recovered (SVIR) epidemic model is proposed to explore the transmission dynamics of rotavirus while capturing memory and hereditary effects associated with disease progression and immune response. The disease-free and endemic equilibrium points of the model are derived, and the vaccination reproduction number Rv is obtained using the next-generation matrix technique. Stability analysis is performed for the disease-free and endemic equilibrium points. In addition, a comparative study for Rv<1 and Rv>1 is presented. The sensitivity of the model parameters is computed, and the results are presented graphically. Also, the positivity and boundedness of the solutions are verified to ensure biological feasibility. The approximate solutions of the Caputo fractional-order SVIR model are obtained using the Laplace Adomian Decomposition Method (LADM). The stability, convergence, and error analysis of this well-established method are also studied. To validate the obtained solutions, the method is compared with other methods in the classical-order case. Additionally, the LADM solutions are presented numerically and graphically for different fractional orders, showing that reducing the fractional-order parameters increases memory effects and significantly changes the epidemic dynamics. The numerical and graphical results confirm that the fractional-order framework captures the dynamics of the proposed model more effectively than the corresponding classical integer-order epidemic model.