Insights and implications of a dynamical systems approach to dengue transmission and epidemic behaviour.

This study introduces a novel dynamical systems framework to investigate the transmission dynamics and epidemic behaviour of dengue fever, offering a deeper understanding of the disease beyond conventional models. While most existing research focuses on basic transmission, this work fills a critical gap by integrating comprehensive stability analysis, bifurcation dynamics, and parameter sensitivity, without relying on control-based strategies. A detailed seven-compartment SEIR-SEI model was developed using nonlinear ordinary differential equations to simulate the interactions between human and mosquito populations. The basic reproduction number R0 was derived, and both disease-free and endemic equilibria were rigorously analysed using the next-generation matrix method to determine the conditions for local and global stability. A key novelty of this study lies in its bifurcation analysis, which reveals the qualitative shift in epidemic behaviour as R0 crosses unity—a phenomenon that has not been deeply explored in prior dengue models. Furthermore, sensitivity analysis using normalised indices and Partial Rank Correlation Coefficients (PRCC) identified the most influential parameters driving transmission, highlighting critical leverage points for disease mitigation. Numerical simulations validated the model with real dengue case data from Bangladesh, demonstrating not only the model’s accuracy but also its ability to predict epidemic thresholds and behaviour. The results indicate that a lower recovery rate (ρ = 0.009) is associated with higher disease prevalence, suggesting that weaker immunity prolongs disease persistence. In contrast, higher recovery rates reduce the spread of infection and help achieve disease control. These outcomes provide valuable insights into the complex dynamics of dengue and offer a robust platform for future research and public health planning.