<p>In the current study, we incorporate saturated incidence, vaccination, and treatment rates into a dengue transmission model to provide a more realistic representation of dengue disease dynamics. The qualitative analysis reveals that both the disease-free and endemic equilibrium points are globally asymptotically stable under certain conditions. The center manifold theory is used to identify the condition under which the model exhibits backward and forward bifurcation. We also explore the occurrence of periodic oscillations in the population through Hopf-bifurcation. We perform a sensitivity analysis to identify the key model parameters that significantly impact disease transmission and control dynamics. Given the high nonlinearity of the proposed model, a dynamically consistent first-order nonstandard finite difference (NSFD) method based on Mickens’ methodology is formulated and used to simulate the system. Additionally, the first-order accurate NSFD technique is combined with Richardson’s extrapolation technique to generate more accurate numerical schemes of higher-order. Various numerical examples are provided and comparison with traditional numerical techniques (Euler and Runge–Kutta of order 4) is detailed to highlight the advantages offered by the proposed NSFD technique. Finally, to validate the model, we use real data from weekly reported cases in Singapore in 2022. This helps us understand the importance of vaccine-related parameters and gives insight into how the disease spreads over time. The findings of this study suggest that NSFD and improved NSFD schemes have the potential to provide more reliable numerical solutions, thereby broadening their applicability to complex real world dynamical systems.</p>