<b>Supplementary </b><b>i</b><b>nformation </b><b>for </b><b>“A novel approach to quantify the optimal range and causal effect of rainfall on vector-borne diseases: A case study of dengue epidemics”</b>

The quantitative relationship between rainfall and the frequency of dengue outbreaks remains poorly understood, with rainfall's contribution often overlooked or mischaracterized. Taking Guangzhou as the case, we develop a dynamic model to identify the optimal rainfall range for mosquito population development. Using mosquito surveillance and meteorological data, we estimate the optimal weekly rainfall range as [131.2mm,212.8mm]. Additionally, we use the DLNM model to analyze the correlation between rainfall and local cases, providing cross-validation. We consequently introduce a novel rainfall index to quantify its causal effects on dengue burden and employ a hurdle regularization model to assess the interplay between imported cases, rainfall, and temperature in shaping dengue outbreaks. The cases in 2014 and 2015 are predicted by fitting the model to epidemic data between 2006-2013. Our proposed rainfall index outperforms existing indices in both model fitting and prediction accuracy. Additionally, switching 2014 and 2015 index values shows a significantly larger 2015 outbreak and smaller 2014 wave, unlike adjustments to temperature or imported case data, highlighting rainfall's dominant role in shaping Guangzhou dengue outbreaks. Although the parameters and the results are restricted to Guangzhou, the fundamental framework can be widely applied to any other region by including the specific data.