Study area and administrative boundaries

Indonesia comprises 34 provinces under pre-2022 administrative boundaries (map of geographical regions are shown in Fig A in S1 Appendix). We excluded four provinces established in 2022 from the reorganisation of Papua (South Papua, Central Papua, Highland Papua, and Southwest Papua) due to substantial missing data. For this study, the Papua region includes Papua and West Papua provinces.

Epidemiological data

We obtained monthly dengue incidence data for 2010–2024 (180 time points) from the Arbovirus Working Team of the Indonesian Ministry of Health and the Open Dengue platform (except final months of 2024) [14]. The data included clinically diagnosed cases of dengue haemorrhagic fever (DHF) reported through Indonesia’s national dengue surveillance system [15,16]. Laboratory confirmation is uncommon, with diagnosis typically based on clinical presentation and basic haematology, supplemented by rapid diagnostic tests where available. We calculated incidence rates per 100,000 population using linear interpolation and extrapolation of 2010 and 2020 census data by age group and sex [17,18].

Climate data

Local climate variables.

We used ERA5-Land reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF) [19], aggregated monthly. Monthly precipitation represents total precipitation (mm). Monthly temperature represents the average daily mean 2-metre temperature (°C). Monthly relative humidity represents the average daily mean relative humidity (%). Relative humidity was calculated from 2-metre temperature (T) and dewpoint temperature (Td) using the formula [20]:

Climate variables were aggregated to the province level using population-weighted averages from the LandScan Global Population Database [21]. Climate data were obtained for 2009–2024 to allow lag calculations using the KrigR package in R [22].

Wavelet analysis

Dynamic time warping (DTW) clustering

We used dynamic time warping (DTW) [26] with hierarchical clustering to identify provinces with similar temporal dynamics, independent of the wavelet phase analysis. Missing case counts were imputed using median monthly proportions within each province. Time series were standardised (z-scores) prior to computing pairwise DTW distances.

We performed three clustering analyses at progressively finer geographic scales: 1) all 34 provinces, 2) western Indonesia, including Kalimantan, and 3) western Indonesia excluding Kalimantan (Sumatra and Java-Bali). Optimal cluster numbers were determined using silhouette scores evaluated for k = 2–15, with consideration of cluster balance to avoid highly unequal cluster sizes. Clustering was performed using the dtwclust package in R [27].

Within-region cohesion analysis

To assess whether administrative regions capture temporal dynamics, we calculated within-region cohesion as the mean pairwise DTW distances among provinces within each region. Lower values indicate greater temporal similarity. Provinces whose dynamics deviate from their regional pattern, using z-scores of mean distances to regional neighbours, with a threshold of 1.645 were identified as outliers (corresponding to 90% confidence level).

Climate-dengue phase relationships

Phase lag and coherence.

We assessed the temporal relationship between climate and dengue using wavelet-based phase angle analysis. For each province and climate variable, we extracted phase angles at the 12-month period and calculated the phase difference with dengue phase angles at each time point. The mean phase lag (in months) shows when climate cycles lead or lag dengue cycles, with positive values indicating climate leads dengue. Phase coherence, quantifying the consistency of this timing relationship over the study period, was calculated as:

where SD is the standard deviation of the wrapped phase differences. Coherence values range from 0 (phase relationship varies randomly over time) to 1 (perfectly consistent timing relationship). Provinces with phase coherence ≥0.85 and positive phase lag were identified as having reliable, predictive climate-dengue timing relationships for early warning applications.

Distributed lag non-linear models (DLNM)

Statistical software

All analyses were conducted in R version 4.5.2 [30]

West-to-east gradient and ecological discontinuity

The west-to-east timing gradient we observed aligns with the progression of the Australian-Asian monsoon system, which moves from northwest to southeast across the Indonesian archipelago [31]. This suggests that provincial differences in peak timing reflect climate-driven seasonality rather than sequential disease spread between provinces. The gradient was strongest when analysis was restricted to Sumatra and Java-Bali (Table 1), and weakened substantially when eastern provinces were included. This indicates that the gradient is a robust feature of western Indonesia but breaks down in the eastern archipelago.

Several factors may contribute to the breakdown of the west-to-east gradient in eastern Indonesia. First, climate regimes differ markedly across the archipelago. Aldrian and Susanto identified three distinct climatic regions in Indonesia: a monsoonal region covering southern Indonesia from Sumatra to Timor, a semi-monsoonal/equatorial region in northwestern Indonesia, and an anti-monsoonal region encompassing Maluku and northern Sulawesi with opposite seasonal patterns [32]. Eastern Indonesia experiences different climate drivers than western provinces, with ENSO and the Indian Ocean Dipole exerting independent, regionally heterogeneous effects on Indonesian rainfall, and the strength of these associations varies by climate region [33]. Indeed, DMI showed stronger associations with dengue incidence than ONI in Maluku and Nusa Tenggara, whereas ONI dominated in western and central regions. This regional heterogeneity in climate index associations may partially explain the breakdown of the west-to-east gradient in eastern Indonesia. Second, surveillance capacity varies geographically. Eastern provinces consistently report lower dengue incidence, and Indonesia’s surveillance system captures only cases presenting to healthcare facilities, potentially underreporting dengue cases, especially in less accessible regions [16]. Notably, the west-to-east gradient was strongest in regions with higher estimated surveillance capacity (Sumatra and Java-Bali), suggesting this pattern may reflect genuine epidemiological dynamics rather than reporting artifacts. Finally, while dengue vectors occur throughout the archipelago [34], serotype distribution and immunity patterns in the population differ between regions and cannot be generalised nationally [35]. Disentangling these climatic, surveillance, and immunological factors requires targeted studies in eastern Indonesia and is beyond the scope of this exploratory analysis.

Heterogeneity within geographical regions

Our clustering analysis revealed that geographical regions are poor proxies for dengue temporal dynamics. Despite geographic proximity, provinces within the same region showed substantial heterogeneity in outbreak timing and amplitude (Fig 3D and Table 2). This has practical implications: regional-level policies may fail to account for province-specific dynamics. The identification of temporal outliers, provinces whose dynamics deviate from their regional neighbours, highlights where province-specific investigation may be warranted, as these outliers may reflect unique local factors such as serotype circulation history [35,5] or vector control programme effectiveness.

Climate-dengue relationships at two timescales

Climate influences dengue at two distinct timescales, each with different implications for preparedness.

At the multi-annual scale, El Niño events were associated with elevated outbreak risk. ONI showed a significant positive correlation with epidemic-year incidence (Spearman ρ = 0.83, p < 0.01), while DMI did not (ρ = 0.33, p = 0.25). Mean incidence during strong El Niño years was 96% higher than during non-strong El Niño years (77 vs 39 per 100,000). This association, while not establishing causality, suggests that ENSO monitoring can inform strategic preparedness such as budget allocation, supply chain planning, and workforce training months in advance of anticipated high-risk periods.

At the annual scale, local climate variables showed province-specific timing relationships with dengue. We focused on local climate rather than large-scale indices for the phase and dose-response analyses because they operate at different timescales: ONI/DMI capture multi-annual ENSO/IOD cycles, whereas local climate exhibits annual seasonality that aligns with the 12-month dengue cycles extracted by wavelet analysis. Local climate also provides actionable signals for tactical interventions at 1–4 month lead times, while ENSO serves strategic planning at longer horizons.

Phase coherence analysis identified provinces where climate-dengue timing was sufficiently consistent for potential early warning applications. Precipitation showed broader utility than temperature, with 18 qualifying provinces (coherence >=0.85, positive or zero lag) compared to 7 for temperature, and 11 significant dose-response associations versus 3. This asymmetry may reflect precipitation’s more direct mechanistic pathway to dengue transmission through breeding site creation, while temperature effects on vectorial capacity may be modulated by other factors that were not explained by the simple model we employed.

Notably, 16 provinces had low phase coherence (<0.70) for all climate variables examined, suggesting that factors other than direct climate effects, such as serotype dynamics, population immunity, or reporting inconsistencies, may dominate their outbreak patterns. For these provinces, climate-based early warning may be less effective than alternative approaches that account for other potential factors.

Complementarity of wavelet and DLNM approaches

The wavelet-derived phase lag and the DLNM-optimal lag frequently diverged (Fig C in S1 Appendix) as expected, because they measure fundamentally different aspects of the climate-dengue relationship. Wavelet phase lag captures when annual cycles align under a sinusoidal assumption, while DLNM identifies the lag with strong or the strongest dose-response effect, allowing non-linear relationships. This divergence supports using both approaches as complementary tools: phase analysis screens for reliable timing relationships, while DLNM quantifies the magnitude of the effects. For West Nusa Tenggara, DLNM revealed a protective effect of high temperature (decreased cumulative RR), illustrating how dose-response analysis may uncover relationships not apparent from timing analysis alone.

For operational early warning applications, these complementary methods provide different actionable information. Phase coherence (wavelet) screens which provinces have reliable climate-dengue timing relationships worth monitoring, while DLNM optimal lag identifies when the strongest lag-dose-response signal occurs for intervention timing. When wavelet and DLNM lags diverge, DLNM lag may be more directly actionable for tactical decision-making as it captures non-linear exposure-response relationships, though prospective operational research is needed to validate this approach.

Implications for early warning

Our findings support a two-tier approach to dengue early warning. The first tier, based on ENSO monitoring, provides strategic warning at 2–6 + month horizons for outbreak years, applicable nationally. The second tier, based on local climate monitoring, provides tactical warning at 1–4 month horizons for seasonal peaks in provinces with high phase coherence. The phase coherence metric may serve as a screening tool to identify where climate-based prediction is most feasible.

Indonesia’s dengue control is largely decentralised, with provincial and district health offices implementing interventions based on local trends, while the national government provides coordination through initiatives such as the 2021–2025 National Strategic Plan for Dengue Control [36]. Our findings support this structure but suggest that inter-provincial coordination, enhanced by coordination and monitoring at the national level, could optimise resource deployment by enabling earlier-peaking provinces to inform preparedness in later-peaking neighbours.

To illustrate, consider North Sumatra (early-peaking, October) and Central Java (later-peaking, February), both with high precipitation phase coherence. In North Sumatra, heightened September rainfall would signal October risk; in Central Java, November–December signals would inform January–February preparedness. This staggered approach could enable more efficient resource allocation than uniform national timing, though prospective validation remains essential.

Limitations

Several limitations should be acknowledged. First, this study is exploratory, aimed at characterising heterogeneous patterns rather than testing causal hypotheses. The associations we report do not establish causality and require prospective validation before operational use.

Second, dengue surveillance quality varies across Indonesia, with eastern provinces likely experiencing greater underreporting than Java and Sumatra. The consistently lower incidence and phase coherence in eastern provinces may partly reflect data limitations rather than true epidemiological differences. Indonesia’s dengue surveillance has used consistent clinical case definitions for dengue hemorrhagic fever throughout the study period [15,16], though laboratory confirmation capacity and reporting completeness have likely improved over time, particularly in western provinces.

Third, the COVID-19 pandemic (2020–2021) likely affected both dengue transmission and surveillance reporting. However, our 15-year study period provides a decade of pre-pandemic data, reducing the influence of pandemic-related anomalies on our findings. Sensitivity analyses excluding 2020–2021 showed that phase lag estimates, phase coherence values, and DLNM associations were qualitatively similar to the full period results (Tables H, I, and J in S1 Appendix).

Fourth, our DLNM analyses modelled each climate variable separately, adjusting only for seasonality, which does not account for correlations between climate variables or potential confounding. Similarly, while we demonstrated strong associations between ENSO (ONI) and multi-annual outbreak patterns, we did not model these large-scale climate indices within the DLNM framework. Such indices may improve predictive power in multivariate models that adjust for the effects of local climate variables such as monthly rainfall, though disentangling these complex delayed effects warrants dedicated investigation. Additionally, the Spearman correlation between ONI and epidemic-year incidence is based on a small sample size (n = 14 epidemic years), and temporal autocorrelation in monthly time series may reduce effective sample sizes and inflate apparent significance of phase-lag correlations. The p-values reported in Table 1 should be interpreted as nominal values given potential autocorrelation structure in the data.

Fifth, the phase coherence threshold of 0.85, while chosen to identify provinces with reliable timing relationships, is necessarily arbitrary. Sensitivity analysis across thresholds from 0.70 to 0.90 showed that the number of provinces with significant DLNM effects remained relatively stable, indicating that our conclusions are not highly sensitive to this choice (Table K in S1 Appendix).

Sixth, we lacked serotype-specific data, a major driver of outbreak dynamics through immunity patterns. Studies have shown that DENV serotype distribution in Indonesia varies substantially between cities and cannot be generalised nationally [35]. This province-level variation in serotype circulation could explain some heterogeneity in climate-dengue relationships. Finally, province-level analysis may mask important sub-provincial variation, particularly in large provinces where district-level dynamics could differ substantially.