Qualitative And Quantitative Aspects Ofâ Dengue Dynamics Using Nonlocal And Non-Singular Kernels

Dengue infection, as a significant public health concern, demands a multifaceted approach that integrates enhanced vector control, public education, robust surveillance systems, and ongoing research into vaccines and therapies. Addressing this growing threat effectively requires collaboration among governments, healthcare organizations, and local communities. In this study, we develop a mathematical model to analyze the dynamics of dengue transmission, offering insights into its pathways for improved control and management. The model employs a novel fractional derivative framework to capture the role of memory effects in transmission dynamics. Our research focuses on both qualitative and quantitative analyses of dengue dynamics. Using Schaefer’s and Banach’s fixed-point theorems, we establish the existence and uniqueness of solutions. The stability of the system is evaluated through rigorous analytical methods. To explore the impact of fractional order, vaccination, treatment, and biting rates on dengue prevalence, we conduct numerical simulations. The results highlight that reducing mosquito bite rates significantly mitigates the severity of dengue infections. Furthermore, the study identifies memory index, treatment, vaccination, and fractional order as effective strategies for controlling dengue outbreaks.