Fig 1.
Study setting and schematic of methodology.
A: Geography of Peru (shaded amber), neighbouring countries and the Pacific Ocean. The three studied departments of Lambayeque, Piura, and Tumbes are highlighted in red, green, and blue respectively, and their capital cities are represented by filled circles. The map was created using the mapview and rgeoboundaries packages in R version 4⋅2⋅1 [21–23]. The base layer map is available at https://www.geoboundaries.org/api/current/gbOpen/PER/. B: Overview of the approach taken for analysis of dengue incidence in the three departments across 2010 to 2021. Details of acronyms used in the schematic and throughout the manuscript can be found in Section 1 in S1 Appendix.
Fig 2.
Dengue incidence rate (DIR) trends over time across the departments.
The monthly DIR per 100,000 is displayed for each of the three studied departments across 2010 to 2011 inclusive. Substantial peaks in monthly DIR occurred in 2015 and 2017.
Fig 3.
Model-based exposure-lag-response relationships between climatic variables and dengue incidence rates.
Plots of relative risk (RR), on a natural logarithm scale, for the included DLNMs (Distributed Lag Non-linear Models) in our climate-based Bayesian hierarchical model for incidence (of new dengue cases) fitted to the entire period of 140 months, where RR is defined relative to the risk induced by the mean observed value of each climate variable. Log RR values greater than 0 (pink to purple) correspond to heightened RR of incidence of new dengue cases, whilst values less than 0 (green) correspond to reduced RR. The four climatic variables were included in the model framework via DLNM specifications alongside temporal random effects, spatiotemporal random effects, and fixed effects (of momentum and seasonality).
Fig 4.
Leave-one-time-point-out cross-validation predictive performance.
Left: The DIR (Dengue Incidence Rate) time series (gold) for each department is shown alongside the posterior median estimate (forest green) for each observation and the corresponding 95% credible intervals of the posterior predictive distributions (shaded grey). Estimates were obtained by refitting the model 139 times, excluding a single time-point/month (of three observations) one at a time, and estimating the posterior predictive distributions for the three omitted observations. Note that due to the presence of temporal autocorrelation terms (such as a random walk of order one prior distribution), leave-one-out predictive distributions for the observations at the first time-point are not generated. Right: The accompanying visualisation displays the observed DIR versus the corresponding estimated DIR, where the filled colours of light red, light green, and light blue represent Lambayeque, Piura, and Tumbes respectively.
Fig 5.
Forecasting predictive performance across 2018 to 2021.
Left: The DIR (Dengue Incidence Rate) time series (gold) for each department is shown alongside the posterior median estimate (forest green) for each observation, and the corresponding 95% credible intervals of the posterior predictive distributions (shaded grey) which were obtained by fitting our model to the climatic and surveillance data up to one month preceding, and estimating the posterior predictive distributions for the next month’s three observations. Right: The accompanying visualisation plots the observed DIR vs the corresponding estimated DIR, where the filled colours of light red, light green, and light blue represent Lambayeque, Piura, and Tumbes respectively.
Fig 6.
Forecasting outbreak detection across 2018 to 2021.
Among the observations with DIR (Dengue Incidence Rate) greater than 50 (left) and DIR greater than 150 (right) per 100,000, the plots depict posterior probabilities of forecasted DIR exceeding thresholds (green) of 50 per 100,000 (left) and 150 per 100,000 (right). The plots capture the model’s sensitivity in forecasting substantial dengue outbreaks one month in advance. To also visually assess the reliability of forecasted outbreaks and ensure a representative picture of our model’s future outbreak detection capabilities, Fig S in S1 Appendix is the analogous visualisation for the corresponding posterior probabilities of the observations with observed DIR less than the thresholds of 50 and 150.
Table 1.
Summary statistics for forecasting outbreak months across 2018 to 2021.
DIR (Dengue Incidence Rate) observations (n = 180) were classified one month ahead of time as being predicted true outbreaks with DIR exceeding 50 (or 150) per 100,000 if the posterior probability of DIR exceeding 50 (or 150) was greater than a cut-off probability of 0⋅21 (or 0⋅13). True Positive measures the hit rate, or equivalently the proportion of true outbreaks correctly detected, whilst False Positive measures the proportion of non-outbreaks incorrectly classified as outbreaks. Accuracy represents the proportion of observations whose outbreak classification matched the true observed state (such as a predicted outbreak coinciding with an outbreak). Precision measures the proportion of predicted outbreaks which were true outbreaks. Finally, the AUC is the area under the Receiver Operating Characteristic (ROC) curve, is used as a measure of our model’s skill for distinguishing between outbreaks. The cut-off probabilities were calibrated using historical data (prior to 2018) and thus, outbreak forecasting model performance is reflective of a realistic application of our framework by authorities. 95% CIs are the corresponding 95% confidence intervals [57, 58]. Further analyses of outbreak classification performance were performed (see Table D in S1 Appendix).