Modeling and analysis of dengue transmission in fuzzy-fractional framework: a hybrid residual power series approach.

The current manuscript presents a mathematical model of dengue fever transmission with an asymptomatic compartment to capture infection dynamics in the presence of uncertainty. The model is fuzzified using triangular fuzzy numbers (TFNs) approach. The obtained fuzzy-fractional dengue model is then solved and analyzed through fuzzy extension of modified residual power series algorithm, which utilizes residual power series along with Laplace transform. Numerical analysis has also been performed in this study and obtained results are shown as solutions and residual errors for each compartment to ensure the validity. Graphical analysis depict the model's behavior under varying parameters, illustrating contrasting trends for different values of ν and examining the impacts of transmission and recovery rates on dengue model in uncertain environment. The current findings highlighted the effectiveness of proposed uncertainty in epidemic system dynamics, offering new insights with potential applications in other areas of engineering, science and medicine.