Time varying methods to infer extremes in dengue transmission dynamics

Abstract

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 70 th (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.

Trade-offs between individual and ensemble forecasts of an emerging infectious disease

“…Fourth, we assumed that the reporting probability was constant through time. Although this is a standard assumption [52] given the lack of data to inform a time-varying relationship for this mechanistic element [53], it would be interesting to include and test a reporting dynamics model (e.g., the reporting probability scales with incidence [54]) as an additional component included in our ensemble framework. Fifth, we conducted this analysis at the departmental level instead of this municipality level, which could obfuscate meaningful differences across regions of a single department [29].…”

“…Around the peak of the epidemic, forecasts from spatially coupled models generally had higher log scores in departments with lower incidence (e.g., Nariño). Later in the epidemic (weeks [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], some models continued to forecast higher incidence than observed in some departments, despite having passed the peak incidence of reported cases (Fig. S16).…”

Toward Scalable Risk Analysis for Stochastic Systems Using Extreme Value Theory

“…We aim to estimate the extremal upper-semideviation of Y ∈ L 1 at level α ∈ (0, 1), which we define by (12) where v α,Y ∈ R is a threshold to be described. Specifically, (13) a common risk functional in finance and operations research [25]. In statistics, v α,Y (13) is called the left-side (1 − α)quantile of Y .…”

“…where y m−k,m is an approximation for v α,Y (13). ρα,k,m (18) is not designed to represent the upper tail of F Y when the number m of samples is limited; we will illustrate limitations of ρα,k,m numerically in Section IV.…”

“…EVT is the study of the long-term behaviour of normalized maxima of random variables. It has been useful for examining extreme events in numerous applications, including hydrology [11], seismology [12], and disease transmission [13]. This theory offers tools to extrapolate beyond the available data to estimate the upper tail of a distribution [14], [15].…”