Abstract / Summary
Motivated by the ongoing public health burden of dengue fever, this study presents a nine-dimensional dengue transmission model that incorporates imperfect vaccination and a phenomenological background effect associated with cryptic habitats. We derive the control reproduction number ( R c ) and examine the global stability of the disease-free and endemic equilibria. To estimate key parameters, we employed a physics-informed neural network (PINN) to fit cumulative dengue death data from Brazil in 2019, achieving a high coefficient of determination ( R 2 = 0.995 ). We then assessed the effects of the vaccination rate, vaccine failure factor, and background parameter n on the transmission threshold. For the parameter set considered in this study, R c decreases with the vaccination rate γ and approaches a positive limit as γ → ∞. The corresponding critical vaccine failure factor is η c ≈ 0.610; when η ≥ η c , vaccination alone cannot reduce R c below one. Ecological observations indicate that cryptic habitats may complicate vector control by harboring mosquito populations that are difficult to detect and eliminate. These results and ecological observations underscore the importance of integrating vaccination strategies with targeted vector control, particularly in cryptic habitats, to effectively mitigate dengue transmission.