Time varying methods to infer extremes in dengue transmission dynamics

Dengue is an arbovirus affecting global populations. Frequent outbreaks occur, especially in equatorial cities such as Singapore, where year-round tropical climate, large daily influx of travelers and population density provide the ideal conditions for dengue to transmit. Little work has, however, quantified the peaks of dengue outbreaks, when health systems are likely to be most stretched. Nor have methods been developed to infer differences in exogenous factors which lead to the rise and fall of dengue case counts across extreme and non-extreme periods. In this paper, we developed time varying extreme mixture (tvEM) methods to account for the temporal dependence of dengue case counts across extreme and non-extreme periods. This approach permits inference of differences in climatic forcing across non-extreme and extreme periods of dengue case counts, quantification of their temporal dependence as well as estimation of thresholds with associated uncertainties to determine dengue case count extremities. Using tvEM, we found no evidence that weather affects dengue case counts in the near term for non-extreme periods, but that it has non-linear and mixed signals in influencing dengue through tvEM parameters in the extreme periods. Using the most appropriate tvEM specification, we found that a threshold at the 70th (95% credible interval 41.1, 83.8) quantile is optimal, with extreme events of 526.6, 1052.2 and 1183.6 weekly case counts expected at return periods of 5, 50 and 75 years. Weather parameters at a 1% scaled increase was found to decrease the long-run expected case counts, but larger increases would lead to a drastic expected rise from the baseline correspondingly. The tvEM approach can provide valuable inference on the extremes of time series, which in the case of infectious disease notifications, allows public health officials to understand the likely scale of outbreaks in the long run.