Unraveling dengue dynamics with data calibration from Palu and Jakarta: Optimizing active surveillance and fogging interventions

Dengue fever is a complex infectious disease driven by multiple factors, including viral dynamics, mosquito behavior, environmental conditions, and human behaviors. The intricate nature of its transmission and outbreaks necessitates an interdisciplinary approach, integrating expertise from fields such as mathematics and public health. In this research, we examine the role of active case finding and mosquito population reduction through fogging in dengue control using a mathematical model approach. Active case finding aims to identify undetected dengue cases, both asymptomatic and symptomatic, which can help prevent further transmission and reduce the likelihood of severe symptoms by enabling earlier treatment. The model was developed using a system of nine-dimensional nonlinear ordinary differential equations. We conducted a mathematical analysis of the equilibria and their stability based on the basic reproduction number ($R_0$). Our analysis shows that the disease-free equilibrium is locally asymptotically stable when $R_0<1$. Furthermore, when $R_0=1$, the model may exhibit backward bifurcation , depending on the death rate induced by dengue. The higher the dengue-induced death rate, the greater the likelihood of backward bifurcation at $R_0=1$. We used dengue incidence data from two Indonesian provinces, Jakarta and Palu, to calibrate the model parameter values. Our global sensitivity analysis on the basic reproduction number indicates that active case findings are more crucial in Palu compared to Jakarta. Conversely, Jakarta is more sensitive to the infection parameter than Palu. Our numerical continuation simulation shows that implementing fogging to control the mosquito population should carefully consider the intensity, timing, and duration of the intervention to achieve a more optimal results.