Spatial Modeling of Climate Change Effects on Dengue Fever Incidence: A Case Study in East Nusa Tenggara

This study was conducted in the East Nusa Tenggara region. The research data consists of secondary data on climate change from database of Meteorological, Climatological, and Geophysical Agency (BMKG), meanwhile the data of dengue fever incidence in the NTT region, obtained from the NTT Provincial Health Office. The data collected is from the year 2022, based on 22 districts/cities.

Meanwhile, the research variables used in this study are detailed in Table 1.

In this study, the spatial weight matrix W used is the Queen Contiguity matrix. This matrix was selected because it considers that adjacent regions have a greater influence on each other. In the Queen Contiguity matrix, spatial units are defined as neighbours if they share a common side or vertex. The research was carried out following a series of methodical steps. First, exploratory spatial data analysis was applied to the research variables to understand the underlying patterns and relationships. This initial a nalysis helps in identifying spatial dependencies and distributions within the data. Next, the study involved constructing a model for regional investments in Indonesia using a spatial panel data approach. Digital map of East Nusa Tenggara Province is shown in Figure 1.

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Figure 1. Digital map of East Nusa Tenggara Province

Table 1. Research variables

2.1 Spatial weight matrix W

The spatial weight matrix W | n×n, with n being the number of regions or the number of observations that must be defined beforehand, is the basis point of the spatial econometric analysis as it describes the impact of the spatial interaction between the regions. It controls what happens in one area, as it is affected by what happens in neighboring areas, so the choice of matrix specification is a critical stage; formally, it can affect the analysis results. For example, the Queen Contiguity uses a matrix where regions that share borders or vertices are treated as neighbors, thus providing more flexibility for spatial definition. However, this method has weaknesses, especially in areas with sparse connections like an island area; sometimes, some regions remain unconnected [20].

The selection of the spatial weight matrix is a crucial aspect, as this plays a critical role in how spatial dependence is captured and the validity of the model. Although the Queen Contiguity matrix is common due to its straightforward interpretation, other approaches, such as distance-based or k-nearest neighbor matrices, may offer greater insights into spatial interactions. Distance-based matrices, for instance, consider geographical distances between sample points; hence, they are very useful in areas where spatial structures are unbalanced. Likewise, k-nearest neighbor matrices guarantee the number of neighbors for each region is a constant number, which is very helpful in solving the problem of isolation in sparsely connected or remote places [21].

The use of a Queen Contiguity matrix here is justifiable by the ability of this type of contiguity to get a direct spatial association at borders or the inclusion of either vertices or boundaries, whilst matching the administrative limit and geographical form of East Nusa Tenggara (NTT). Alternative approaches, such as distance-based matrices, were contemplated, but ultimately not adopted, as the region has a wide geographic scale, and establishing adequate distance thresholds in a heterogeneous topography is challenging.

Also, the selection of the Queen Contiguity matrix bears a direct impact on the outcomes of this research. It guarantees that spatial dependencies, such as spillover effects of climate variables, occur within districts that are close to each other. This decision affected how the spatial error model (SEM) performed, enabling the SEM to detect spatially correlated errors associated with unobserved elements, like endogenous population movement or local characteristics of mosquito habitat. Nonetheless, it should be noted that this matrix does not capture long-distance interactions or spatial dependence beyond immediate neighbors, which may result in underestimating spatial effects that act more globally.

The results also suggest the exploration of alternative matrices, like hybrid matrices that integrate contiguity and distance, in future research to give researchers a more nuanced understanding of how spatial relationships interact. The hybrid matrices can represent both direct and indirect interactions between regions and produce better results in geography that is complicated like NTT. This would improve knowledge of the local drivers of dengue fever transmission and form a robust basis for targeted public health action.

The matrix is defined as:

$w_{i j}= \begin{cases}1, & \text { if regions } i \text { and } j \text { are neighbors } \\ 0, & \text { otherwise }\end{cases}$

To ensure consistency across regions, w is row-standardized, meaning that each row of w sums to one. This standardization transforms the weights to:

$w_{i j}^*=\frac{w_{i j}}{\sum_{j=1}^N w_{i j}}$            (1)

where, $w_{i j}^*$ represents the standardized spatial weight for neighboring region pairs.

2.2 Basic regression model

We start with the basic Ordinary Least Squares (OLS) model that explains the relationship between the independent variables and the dependent variable, ignoring any spatial effects.

$Y_i=\alpha+\sum_{k=1}^3 \beta_k X_{i k}+\epsilon_i$           (2)

where,

$Y_i$ is the observed value of the dependent variable (dengue fever cases) for region i.

$X_{i k}$ represents the independent variables for region $i$, including temperature $\left(X_1\right)$, humidity $\left(X_2\right)$, and rainfall $\left(X_3\right)$. $\alpha$ is the intercept term.

$\beta_k$ are the coefficients for the independent variables.

$\epsilon_i$ is the error term for region i.

2.3 Testing for spatial autocorrelation: Moran’s I

To determine whether to accommodate spatial effects in the model, we test for spatial autocorrelation in the residuals from the OLS model with Moran's I, a common test of spatial autocorrelation based upon a statistic that demonstrates whether similar values group in the space. A strong Moran's I statistic indicates that the residuals are spatially autocorrelated, which means that there are significant spatial dependencies in the data and the use of standard OLS regression is not an appropriate technique. This is illustrated by the presence of spatial autocorrelation, whereby not only are observations in neighboring regions not independent, but rather the relationships between variables may cross spatial boundaries [18]. This can be done by incorporating spatial effects in traditional econometric models, such as spatial autoregressive (SAR) or spatial error models (SEM) [22].

$I=\frac{N \sum_{i=1}^N \sum_{j=1}^N w_{i j}\left(Y_i-\bar{Y}\right)\left(Y_j-\bar{Y}\right)}{\sum_{i=1}^N\left(Y_i-\bar{Y}\right)^2 \sum_{i=1}^N \sum_{i=1}^N w_{i j}}$             (3)

where,

N is the total number of regions.

$\bar{Y}$ is the mean value of Y.

$w_{i j}$ denotes the spatial weight between regions i and j. A significant Moran's I statistic indicates spatial autocorrelation in the data, suggesting that the standard OLS model is inadequate and a spatial econometric model is necessary.

2.4 Spatial econometric model development

Since Moran’s I suggests that there are spatial autocorrelations, we extend the OLS model by incorporating spatial effects. The dependence of observations on other observations can be included in two main ways, via the spatial lag of the dependent variable or the spatial autocorrelation in the error term.

Step 1: Implementing the spatial lag model (SAR)

The first extension adds a spatially lagged dependent variable. This method shows the impact of the other regions on the active region. The equation is:

$Y_i=\rho \sum_{j=1}^N w_{i j} Y_j+\alpha+\sum_{k=1}^3 \beta_k X_{i k}+\epsilon_i$            (4)

where,

ρ is the spatial autoregressive coefficient, indicating the strength of the spatial dependence.

$\sum_{j=1}^N w_{i j} Y_j$ represents the spatially lagged dependent variable that accounts for average values of adjacent areas.

The SAR model is obtained by incorporating the term ρWY into the OLS model, thus making Eq. (1) into Eq. (4), where the spatial influence is explicitly involved.

Step 2: Spatial error model (SEM)

Or it can be modeled as spatial dependence in the error term. In this model, known as the spatial error model (SEM), spatial correlation is specified in the residuals, which also means that unobserved variables that affect the incidence of dengue fever are spatially correlated between regions. The SEM is represented as:

$Y_i=\alpha+\sum_{k=1}^3 \beta_k X_{i k}+\epsilon_i$              (5)

$\epsilon_i=\lambda \sum_{j=1}^N w_{i j} \epsilon_j+u_i$              (6)

where,

λ is the spatial autoregressive parameter for the error term.

$u_i$ is an independent error term that follows a normal distribution.

In this model, the error term $\epsilon_i$ is influenced by the spatially lagged error from neighboring regions $\sum_{j=1}^N w_{i j} \epsilon_j$. This approach assumes that the spatial effects originate from the unobserved variables rather than the observed variables.

2.5 Model selection criteria

Selecting the appropriate spatial econometric model (SAR vs. SEM) is a key element of spatial data analysis. This choice has a major impact on capturing spatial dependencies correctly, which ultimately leads to accurate and interpretable information about the data. While torque is used by-group in almost all statistical models, researchers often test their data with a variety of model evaluation criteria to make sure that their selection is consistent with their data.

The most popular tests to achieve this are the Lagrange Multiplier (LM) tests, the LM Lag Test, and the LM Error Test. Assessment of how the spatial dependencies are embedded in the data. The LM Lag Test examines the parameter of nominal spatial lag (ρ) to determine if there are direct spatial interactions that may influence the dependent variable. A substantial result means spatial effects have a direct influence on the dependent variable, making the SAR model more adequate. Note that the LM Error Test checks the spatial error parameter (λ) to determine spatial autocorrelation in the residuals. If the result of the LM Error Test is significant, the SEM is preferred because it incorporates this type of spatial dependency better [14].

As a consequence, the results of these tests often seem to make the decision cut and dry. If the LM Lag Test is significant and the LM Error Test is not, a SAR model better captures spatial interdependence since it focuses on such interactions in the dependent variable. In contrast, if the LM Error Test is significant while the LM Lag Test is not, then SEM is more appropriate, since it aims at capturing spatial correlations in the residuals. Spationomic models have the advantage that researchers can adjust their models to the realistic spatial structure of the data [17].

Still, ambiguity may arise if both tests yield significant results, which indicates spatial dependencies can exist for both the dependent variable and residuals. When this is the case, researchers frequently resort to robust variants of the LM tests, which account for possible overlaps between the two types of spatial effects. Also, model selection criteria (e.g., Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC)) can assist in the decision-making process. These criteria are designed to evaluate the fit of the model while applying a penalty for developing complex models [23].

Finally, the decision of whether to use SAR or SEM depends on statistical tests, model fit indices, and the nature of spatial dependencies present in the data. Combining these techniques gives researchers the ability to have robust results while capturing the complexities of the spatial relationships. This process is essential for estimating spatial econometric models that are explicitly meaningful and practically useful.

2.6 Model estimation techniques

Spatial econometric models, including the spatial autoregressive (SAR) and spatial error models (SEM), utilize robust estimation techniques to model the spatial dependencies inherent in the data. There are two common approaches to estimating the model parameters, including the spatial autoregressive coefficient (ρ), spatial error coefficient (λ), and regression coefficients (βk): Maximum Likelihood Estimation (MLE) and Generalized Method of Moments (GMM). The choice of method depends on the whisker of the data and what the analysis should achieve. MLE is a technique that maximizes the likelihood function of the observed data conditioned on a certain distribution of the error term. When the assumptions of normality and homoscedasticity are satisfied, this is a very efficient way of doing it. Under such conditions, it yields uniform and efficient estimates of the function parameters. However, MLE provides computational challenges, specifically with matrix inversion of the form (I−ρW), which can be computationally intensive in cases of large data set or complex spatial structures. Generally, such approaches require sophisticated computational resources to guarantee the applicability of the method [22]. GMM is a more flexible approach where we do not need strong assumptions on the error term distribution. Instead, it uses population moment conditions that can be obtained from the model to estimate parameters. Its flexibility also makes it particularly appropriate for situations where the data exhibits heteroskedasticity or departures from normality. In addition, GMM has lower computational costs than MLE, since it does not require the direct inversion of large spatial matrices. Already established empirical studies have shown that GMM offers a stable performance in the spatial econometric context, even more with data sets with highly spatially varying data [24]. In contrast, MLE's advantage remains for datasets for which the error structure conforms to normality assumptions, as it yields highly-efficient and accurate parameter estimates [25]. When it comes to deciding which estimation technique to use, it should be based on the question we want to answer and the data we have. MLE, on the other hand, is more suitable for applications that emphasize estimation accuracy from correctly specified distributions, whereas GMM offers more flexibility and resilience when data is problematic, like heteroskedasticity or non-standard distributional errors. These contrasting properties reflect the complementary functions of MLE and GMM within the scope of spatial econometric analysis. Both MLE and GMM are critical for SAR and SEM models.

2.7 Diagnostic checks and interpretation

Once you fit a spatial econometric model, it is important to conduct diagnostic checks for the model and multicollinearity. Hence, those checks would also indicate that something went wrong-if any were going wrong-e.g., in case of multicollinearity, non-normality of the residuals, presence of the residuals' spatial autocorrelation, et cetera. These diagnostics guarantee the robustness of results when analyzing complex phenomena such as dengue fever incidence in East Nusa Tenggara.

The first step in a diagnostic process is to check multicollinearity in the independent variables. This phenomenon in multiple regression is known as multicollinearity, whereby two or more predictors are highly correlated, leading to inflated estimates of their coefficients and making the causal relationships harder to interpret. Tools such as Variance Inflation Factor (VIF) are often used to check for this problem. Flagging high VIF scores indicates that some collinearity issue exists and that we should prepare to address it by either merging correlated variables or dropping the redundant ones. This applies to climate variables, like temperature and rainfall, that may inherently have interdependence.

Another important diagnostic of whether or not the standard linear regression assumptions hold true is checking the normality of the residuals. Residual normality is an assumption of many spatial econometric models, especially those implemented using Maximum Likelihood Estimation. Violations of normality can lead to inaccurate parameter estimates and invalid tests of inference. Tests such as the Shapiro-Wilk test can be conducted to assess residual normality, or residuals can be observed graphically with quantile-quantile (Q-Q) plots. Transformations or robust estimation techniques may be necessary if the residuals do not conform strictly to normality [26].

The third key diagnostic is used to check for remaining spatial autocorrelation in the residuals. Just like in traveling salesman problems, if residuals are still spatially correlated, it means your solution has not found optimal parameters for your model to capture spatial dimensions. Moran’s I statistic is a classic tool to investigate the spatial autocorrelation of residuals. However, the identification of spatial dependence implies the necessity for model improvement, for example, through additional spatial lags or error terms. In the context of a dengue fever model, for instance, failing to address spatial dependencies likely indicates missing factors (e.g., population density, healthcare access within the area) affecting the distribution of the cases [14].

With careful execution of these diagnostic checks and addressing any issues, the spatial econometric model is a potent vehicle for insight into complex dynamics. In the case of dengue fever, such a model could help show how the climate factors interact with the spatial dependencies to create patterns of disease. For example, increased rainfall may not only favor local mosquito breeding but also induce "spillover effects" in adjacent regions via human or vector mobility. Addressing all diagnostic issues ensures that researchers will provide more robust and useful knowledge to shape public health efforts.

Diagnostic checks are critical to validating spatial econometric models. Through steps like addressing multicollinearity, ensuring the normality of residuals, and accounting for spatial autocorrelation, researchers can develop more nuanced models and provide findings that accurately reflect the spatial dynamics highlighted in their data.

2.8 Latest research in the field of climate change and dengue transmission

Climate change has become an increasingly critical factor driving the emergence and reemergence of vector-borne diseases (VBDs), such as dengue fever, over the past decades. The link between climate change and the global proliferation of these diseases is well-documented. The study [27] emphasizes that global warming, when coupled with urbanization and rising greenhouse gas emissions, has facilitated the expansion of mosquito populations into regions previously unsuitable for their survival. Changing weather patterns such as variations in temperature, precipitation, and humidity play a pivotal role in shaping the habitats and breeding cycles of these vectors, thereby amplifying the risks of dengue transmission.

To address the challenges posed by the spatial and temporal dimensions of dengue transmission, researchers have employed a variety of modelling techniques. The study [28] utilized geostatistical methods, including binomial kriging, to map the prevalence of dengue fever in Khyber Pakhtunkhwa, Pakistan. Their findings revealed that dengue outbreaks were particularly concentrated in low-altitude regions, with Peshawar experiencing the highest burden of cases. The study identified critical risk factors such as population density, proximity to roads, and vector distribution, which provided valuable insights for targeted public health interventions in the region.

The relationship between climatic factors and dengue incidence has also been explored through geographical information system (GIS)-based approaches. For example, the study [29] analysed the spatial and temporal distribution of dengue cases in Sri Lanka from 2009 to 2014, discovering a significant positive correlation between rainfall and dengue incidence. Interestingly, their study did not find a similar correlation for temperature or humidity. Similarly, the study [30] investigated the epidemiology of dengue in Bangkok, Thailand, focusing on seasonal patterns and their association with climatic factors. Through Spearman correlation and multivariate Poisson regression analyses, the study demonstrated that humidity and rainfall were significant contributors to dengue transmission. A 1% increase in rainfall was associated with a 3.3% rise in dengue cases, underscoring the critical role of weather variables in the region's dengue dynamics.

In Pakistan, the study [31] used GIS mapping and generalized linear modeling (GLM) to study the spatial intensity and significant factors associated with dengue outbreaks. The results showed that rainfall, temperature, and access to healthcare facilities were significant determinants of dengue prevalence. The study also revealed that 2011 was the most devastating year during the 2006–2017 study period, with 290 fatalities attributed to dengue in Pakistan. This highlights the potential of spatial models to identify high-risk areas and improve resource allocation for disease control.

In the meantime, Bayesian approaches have further advanced the understanding of dengue fever dynamics by incorporating both spatial and temporal autocorrelations. The study [32] reviewed the use of Bayesian spatial and spatio-temporal models for dengue, emphasizing their superiority over frequentist methods in handling complex data structures and uncertainties. The study [33] applied these methods to study dengue risk in Puerto Rico, revealing significant lagged effects of temperature and precipitation on dengue incidence, with delays of up to four and three months, respectively. Their work provided actionable insights for designing targeted interventions. Similarly, the study [34] explored the effects of forest loss, precipitation, and temperature on dengue in Mexico, finding that a 1% decrease in forest cover was linked to a 16.9% increase in dengue risk. The study [35] expanded this focus by using downscaled climate models to predict spatial and temporal shifts in dengue transmission suitability under future climate scenarios in Pakistan. Their findings highlighted the need for adaptive strategies as climate change alters the landscape of dengue risk.

Expanding the scope of analysis, the study [36] incorporated both environmental and socioeconomic factors into a generalized additive model (GAM) to examine the spatiotemporal patterns of dengue fever. The study demonstrated that while environmental factors, such as temperature and precipitation, exhibited slight variations across regions, socioeconomic variables like population density, land use, and road density played a more pronounced role in determining the incidence of dengue fever. Zheng et al. [36] concluded that resources for prevention and control should be allocated based on the spatial patterns of primary influencing factors to maximize the effectiveness of interventions.

In the context of East Nusa Tenggara, this study seeks to understand the spatial relationship between climatic factors and dengue incidence using spatial regression modeling. This method provides a simpler yet effective framework for analyzing spatial dependencies and understanding how climatic factors influence disease transmission.

The Universal Kriging method employed in this study enables the estimation of climate variables in Nusa Tenggara Timur (NTT) at a given location based on observations from surrounding locations while accounting for global trends or systematic variations. Universal Kriging explicitly accounts for spatial trends, allowing it to estimate for unmeasured districts in a region with extensive gaps in weather stations. Studies in mountain areas found Universal Kriging to improve significantly upon the interpolation of temperature and rainfall data and allow for more accurate assessments of climatic effects on the local ecosystem. This is important in areas with heterogeneous climate conditions, where localized microclimates can have a large impact on disease transmission dynamics [37]. The consideration of spatial variability and trend in the summary of climate data is more meaningful to represent whether climatic conditions are related to the spread of DBD compared with simple interpolation methods that would fail to capture such a relationship.

Example or evidence, in a study comparing Universal Kriging with other interpolation methods [38-40] the authors reported that Universal Kriging performed better both in terms of minimizing interpolation errors and capturing the spatial trends, especially in regions where the topography is complex or the climate is heterogeneous. Differences in temperature, humidity, and rainfall throughout NTT are correlated to the diversity of dengue fever cases found across the region, the study found. Other studies reported that there is a negative correlation between temperature and incidence of dengue. This mirrors patterns of dengue globally, in other tropical regions where cooler temperatures are associated with extended mosquito life cycles as well as greater virus survivability. Yet the study did not establish precise temperature thresholds, suggesting one potential direction for future studies would be to delineate specific ranges that have substantial effects on transmission dynamics.

This is in line with findings in other tropical areas, in which decreased temperature has been associated with increased incidence of dengue due to prolonged longevity of mosquitoes and higher survival. Lower temperatures, however, may also result in higher humidity, leading to ideal breeding conditions for the Aedes mosquito. Similar results have been observed in studies conducted in Thailand and Brazil, indicating that the relative humidity and temperature should be cool and wet for better survival and reproduction of mosquitoes [41].

The sensitivity of the study between humidity and dengue incidence is weak, due to the impact of other environmental factors, that hit harder than humidity. Although high humidity is often understood to correlate to optimal conditions for mosquitoes, temperature fluctuations, rainfall variability, and socio-environmental dynamics (e.g., urban density, water management practices, and waste disposal systems) might exert a stronger influence on dengue transmission. However, poor water storage and drainage lead to abundant ideal breeding conditions resulting in increased mosquito populations irrespective of humidity level. Studies in Malaysia and Singapore indicate that while humidity facilitates mosquito life cycle development, temperature and rainfall patterns exert a larger influence on mosquito population dynamics and transmission rates of the virus itself. Socio-economic factors like urban planning and housing density are also crucial in this aspect. Poor waste disposal and a lack of proper urban drainage can worsen conditions for mosquito breeding, even in humid highland areas. Thus, although humidity is conducive to mosquito propagation, it might not be the most important factor associated with dengue incidence in NTT.

In contrast, rainfall did not correlate well with the distribution of dengue cases. Another interesting note about why these areas may not face such high mosquito breeding rates could be related to better drainage systems or local practices related to vector control aimed at limiting standing water that leads to elevated breeding rates of mosquitoes. Moreover, heterogeneities in infrastructure and public health interventions may mask the expected impact of rainfall on dengue transmission.

Several previous studies reported that rainfall contributes to breeding sites for mosquitoes, but the overall spatial distribution of dengue cases may correlate with other factors better than rainfall, such as temperature, population density, and local environmental conditions. Similar observations have been made in Colombia [42], where areas with higher rainfall were not necessarily places with a higher number of dengue cases, possibly as a result of differences in vector control strategies and local environmental determinants. Particular approaches like the frequent application of larvicide, desirable drainage maintenance, and the implementation of community-based mosquito source reduction programs could determine whether high rainfalls can be avoided, increasing the risk of dengue transmission.

Results of our spatial regression analysis, which included Moran's I and Lagrange Multiplier tests, showed that we had spatial dependencies in our data that called for the use of spatial econometric models. The strong spatial error dependence indicates that unobserved factors that influence dengue cases have spatial dependence. Unmeasured covariates may include sociodemographic conditions, such as income levels and housing quality, accessibility to health services, or undocumented local measures such as community-led vector control programs or environmental management practices. Incorporating and recognizing such variables could help improve the strength of spatial models. As derived from the Akaike Information Criterion (AIC) value and R² statistics, the well-performing model was the spatial error model (SEM) over Ordinary Least Squares (OLS) and Spatial Autoregressive Model (SAR). The comparative AIC and R² values for each of the four models are summarized in visual representation of the analytical data from Table 1, which was drawn from using R. This finding is consistent with other studies that have preferred to use SEM for modeling health outcomes influenced by environmental exposures where residual spatial autocorrelation needs to be taken into account [43].

Temperature was negatively associated with dengue incidence, meaning that dengue incidence in NTT increased as temperatures decreased. This conclusion fits with the observations from other tropical regions with cooler temperatures, which also elongate the lifespans of mosquitoes and also lengthen the period between infection and transmission of a virus. The specific geographic and climatic traits in NTT with its numerous microclimates and large climatic oscillation may enhance this relationship differently compared to other places. Although this relationship was noted in other studies, which find that cooler temperatures extend mosquito life expectancy and therefore also the extrinsic incubation period of the virus, thus increasing potential for transmission [44]. Our findings are in line with these observations and indicate that effective temperature control measures would likely be central to break dengue transmission in the cooler regions of NTT.

The low value of the spatial lag parameter in the SAR model indicates that the impact of cases in neighboring districts on those in a given district is small. The unique geographical characteristics of NTT islands, the distance between islands, and their diverse topography, could be one of the contributing factors to the continuity of its decentralized development as this led to limited connectivity and human mobility between districts. Moreover, socio-political aspects such as differing levels of expenditure for vector control and public health measures may indirectly lead to this lack of effective influence by fostering discrepancies in dengue prevention between districts. These findings suggest that dengue transmission may be more spatially localized and driven by predictors unique to the level of querying districts (local environmental conditions, population density, and health interventions) than those from neighboring districts. Similar conclusions have been drawn from studies conducted in Mexico and Vietnam, where localized factors had a greater influence on dengue transmission than spatial spillover effects.

We conclude that based on this study's results that the SEM is the most appropriate model used to obtain spatial distribution on dengue cases in NTT. From the comparison of the OLS, SAR, and SEM models, it was proven that SEM is the model that best suits the analysis of the spatial distribution of dengue cases in East Nusa Tenggara (NTT) proven by the lowest AIC value and the highest R². Table 2 provides a summary of the comparative AIC and R² values across the models, visually reaffirming the superior performance and applicability of SEM to spatial analysis for this study. Thus, the minimum AIC value points out that SEM fitted best to the data without being overfitted while maximum R² shows its superior capability of explaining the variance of dengue cases by some climatic and spatial factors. This indicates the ability of SEM to handle cross-spatial relations that are missed by simpler models like Ordinary Least Squares (OLS) and even the Spatial Autoregressive Model (SAR).

This field relevance may also be supported by the spatial autocorrelation of the OLS model residual spatial analysis and the results of the Moran’s I test. This suggests that unobserved factors such as breeding habitat, population density, or environmental management may not be accounted for with OLS or SAR. This spatial dependency is accommodated in a spatial error component model (SEM), which thus provides for superior robustness and accuracy of the estimates [43]. This result is consistent with earlier studies highlighting the utility of SEMs for modeling spatially autocorrelated environmentally mediated health outcomes [14, 43].

The results of the comparison between OLS and the two spatial regression models (SAR and SEM) also showed that the SEM was the most appropriate model to assess the spatial distribution of cases in NTT, as reflected in the lowest AIC and the highest R². Additionally, the SEM model, due to this spatial error dependence, indicates that dengue management would need to be tailored around the peculiarities of those specific districts. In this study, for example, low temperatures were positively significantly associated with dengue cases. The association underscores the importance of implementing targeted interventions in districts with low temperatures during the colder months, where the conditions prolong mosquito lifespan and prolong the extrinsic incubation period of the virus [44]. Along the same lines, cooler and wetter climate conditions clinically increased dengue transmission in Thailand and Brazil as increased Aedes aegypti mosquito survival and proliferation [41].

On the contrary, the performance of the SAR model is not better than SEM in this study. In contrast, the spatial lag parameter in SAR had a minuscule effect, indicating that the distribution of dengue cases is less dependent on direct spillover effects of dengue from neighboring districts and more dependent on local factors. This pattern indicates that dengue transmission in NTT is more influenced by local processes (i.e., microclimatic differences and water management practices) than by regional-level scatterings and interaction. Interestingly, in studies from Vietnam and Mexico, local socio-economic and environmental characteristics were found to be more influential in shaping patterns of dengue transmission than effects of spatial spillover [42].

Thus, the implementation of SEM within this work has important implications for public health approaches. The SEM model's capacity to control for spatial error dependence underscores the importance of targeting interventions based on district-specific features that increase the risk of dengue. Some types of interventions include the targeted delivery of vector control, including insecticide spraying and larvicide application in high-risk districts, or social sector interventions/health infrastructure improvements, such as drainage enhancement to mitigate standing water. These measures can be adapted depending on the specific environmental and socio-economic conditions of each district. Districts with lower temperatures, for instance, need to ramp up vector control activities during cooler months. Localized interventions are crucial in breaking the transmission cycle and limiting the potential for dengue outbreaks. These recommendations are consistent with those from other studies in Southeast Asia, which highlight the need for localized dengue control strategies based on district-specific conditions [45].

This study shows that the SEM model is the best choice for modeling the spatial pattern of NTT dengue cases. Based on the AIC effect and R² comparison of OLS, SAR, and SEM, it was found that SEM is the most appropriate model to see the spatial distribution of dengue cases in NTT. SEM reveals additional localized insights into dengue transmission drivers, pointing towards the necessity of district-specific interventions as it accurately captures spatial error dependence. These results are consistent with more extensive investigations that highlight the importance of spatial models for elucidating the role of climatic, spatial, and socio-environmental parameters in determining the risk of diseases [14]. This use of SEM not only deepens the understanding of the complex dynamics of dengue fever transmission in geographically diverse regions such as NTT but also provides a framework for guiding public health interventions at local, provincial, and national levels.

The spatial error model (SEM) is a statistical model that is used to analyze spatial dependencies between regions in a dataset. This method was applied in this study to analyze directly and indirectly how temperature affects the transmission of dengue fever in East Nusa Tenggara (NTT). While the p-value for temperature (0.08927) indicates that temperature is weakly statistically significant, it is the practical significance of temperature that should not be neglected. For the primary vector of dengue fever, the Aedes aegypti mosquito, temperature is an important determinant of its lifecycle. It also affects how mosquitoes reproduce and how the virus develops inside a mosquito. Temperature is a key predictor of disease risk in a context like NTT with high climate variability.

The coefficient for spatial error (λ=−0.217, p=0.481) in SEM indicates the absence of statistically significant spatial dependencies. This indicates that the regional interconnections that previously facilitated the spread of dengue cases, as measured using this model, do not have a significant impact on those previously observed data, or that other factors not measured were influencing the spread. Spatial dependencies may account for factors such as human movement between districts or differences in environmental characteristics such as open pools of stagnant water or amounts of vegetation, both of which are critical for mosquito breeding. Due to the diverse landscape and unequal infrastructure crisis in NTT, the risk of disease is usually unequal in the region.

The poor model temperature-case relationship might also suggest that the model is missing important variables, such as rainfall, humidity, or socio-economic variables. NTT has seasonal rainfall patterns which lead to formations of breeding sites for mosquitoes. And, in cooler times, the mosquito lifecycle may slow but the efficiency with which the virus spreads in the mosquito may actually increase, highlighting the complexity of the temperature-disease relationship. Even with weak statistical significance aside, temperature is an important consideration in assessing the risk of dengue in the region.

The study underlines the need for the use of data in making decisions that work towards averting the risks of dengue with district-level early warning systems that involve climate and spatial data. For instance, in cooler or wetter times, aerosol insecticide spraying or source reduction campaigns could be emphasized in high-risk areas. Future studies should also include variables such as poverty levels, population density, and access to clean water in order to increase model accuracy. Including projections of climate change could also help to understand how the risks of dengue may change over time. This will not only provide a depth of analysis but also an actionable insight that can feed into planning for health on the ground to formulate a mechanism to live up to vector-borne diseases in NTT more dynamically.

The results of this study highlight the importance of temperature in the determination of dengue incidence in NTT. This is especially important as climate change has been predicted to amplify temperature fluctuations, potentially leading to more days of vulnerability and more instances of dengue outbreaks. This finding helps to explain the observed association between cooler temperatures and greater dengue incidence and suggests that health authorities should consider implementing targeted interventions during cooler periods to reduce dengue risk. This method could, for example, facilitate enhanced vector control measures in the lead-up to and throughout the cooler months to reduce the abundance of mosquitoes and interrupt the transmission cycle.

The weak correlation of humidity and rainfall and distribution of dengue case in the current study indicates that while those factors help to create breeding grounds, the two variables may not act as good predictors for outbreaks, which is also true in the case of a previous study conducted in NTT [46]. These results are consistent with findings from tropical areas such as Colombia and India, showing that rainfall did not predict outbreaks alone, as drainage systems, and locally delineated vector control measures were effective. Yet, the distinctive climatic and geographic characteristics of NTT, including its marked microclimates and uneven infrastructure, may further modulate the influence of these factors, necessitating region-specific analysis. This result aligns with previous analyses that have found temperature to be a more significant driver of dengue risk than humidity and precipitation. Thus, the monitoring and controlling of temperature should be a priority of public health interventions so that the changes in dengue risk could be predicted and properly addressed.

While these findings offer valuable insights into the spatial dynamics of dengue fever in NTT, there are some limitations that need to be acknowledged. The interpolation of climate data could be affected by the scarcity of weather stations, thus influencing the accuracy of the Universal Kriging method. In order to overcome this limitation, additional data sources, such as satellite-based calculated climate data or reanalysis datasets, could be incorporated. These sources provide higher spatial and temporal resolution to better interpolate climate variables and assess their influence on dengue transmission. In addition, these findings must be interpreted carefully as they represent probabilistic and not deterministic relations. This level was statistically significant but may not sufficiently describe the relationships between the many factors that drive dengue incidence. The use of incomplete or incomplete spatial data is also known to influence the prediction accuracy of climate-influenced diseases [47].

Socio-economic factors (such as income level, housing conditions, and access to healthcare services) and mobility/migration patterns can be potential confounders. They are considered to influence the vulnerability and exposure of populations to vector-borne diseases. For example, one study shows that areas with limited access to healthcare facilities and congested living conditions have a high vulnerability to dengue fever offenses [48]. Furthermore, high mobility results in the potential dispersal of infected individuals or vectors between areas [49]. Furthermore, inequitable socio-economic factors also affect the utility of vector control programs, and it is shown that under-resourced communities are less likely to benefit from interventions.

Local vector control practices, which were not accounted for in this analysis, are also a key factor that modulates the dynamics of dengue transmission. Community engagement has also shown to be beneficial for vector control programs with a case study in the developing world exemplifying that there is a reliance on community support for vector control efforts and the sustainability of interventions [50].

Further studies should have more holistic and robust spatial models by incorporating socio-economic factors, mobility trends, and local actions. Potential data sources may include census data with data on socio-economic variables such as income and housing quality, health facility access records, migration measures from transport or cellphone network data. Integrating these data would greatly improve the predictive power and contextual relevance of the models. Such analysis would not only improve our predictive models but also better inform the drivers of dengue disease burden in this location. These results reinforce the importance of a multidimensional approach to studying vector-borne diseases in tropical regions [23]. Additionally, future research could delve into the application of other spatial econometric frameworks, including Geographically Weighted Regression (GWRs), to acknowledge potential non-stationary spatial interdependencies across diverse administrative units. GWR could say more about the socio-environmental variables that contribute to dengue transmission that are specific to a given dataset, and therefore help direct more localized interventions. In addition, the incorporation of climate projections into the models can help inform our understanding of how climate change can impact dengue transmission and support longer-term public health planning.

Results showed that temperature is the main weather determinant of dengue transmission in NTT, while humidity and rainfall have minimal variable significance. These results signify the necessity of place-specific interventions and suggest that spatial dependencies could be captured using a spatial error model, which was found to be the best performing model in this context. These results help to better explain dengue dynamics in the region and ensure that spatial heterogeneity is better accounted for in disease prevention strategies.

This study's findings indicate that climate change, especially temperature and precipitation changes, have a significant effect on the spread of dengue fever in East Nusa Tenggara (NTT). These environmental factors affect the lifecycle of the Aedes aegypti mosquito, including its reproduction rate and the ability for the virus to thrive in the mosquito. Considering these results, community-based public health approaches are vital in mitigating the effects of climate change on dengue fever. Such strategies must prioritize early warning systems, environmental management, and community awareness to build understanding of the links between climate change and health risks.

Perhaps the most effective one is to establish a climatically based early warning system to alert when dengue fever is likely to outbreak. Using data about temperature, precipitation, and humidity, the authorities can now identify periods of heightened risk in advance, enabling them to take preventive measures. For instance, such an information system can help guide the timing of insecticide spraying campaigns, community clean-up drives, or the distribution of protective measures such as mosquito nets in areas at risk for an outbreak. Early warning also helps disseminate information to the public on measures they can take to prevent mosquito breeding, such as covering containers where water is stored or clearing stagnant water near their households.

Another preventive strategy is environmental management to minimize the risk of dengue as more rain and stagnant water rise due to climate change. Building an efficient drainage system and improving waste management infrastructure can help eliminate potential mosquito breeding sites. Community participation is critical in this initiative, which includes periodic clean-up drives to remove potential breeding habitats such as used containers and to desilt blocked drains. Ensuring that communities are empowered to manage and monitor their environments means that efforts to control mosquito habitats will be sustainable and effective.

Public awareness is essential for the success of these strategies. Teaching communities how climate change worsens dengue outbreaks can help them understand the need for preventive measures. Health education campaigns in culturally diverse areas such as NTT should be adapted to local practices and traditions. Using community leaders, health volunteers, and women’s groups, the messaging will reach all levels of society. Practical tips, including the use of natural larvicides, covering water tanks, mosquito screens, etc., can be localized and presented on platforms where people can relate to them and adapt them easily.

Lastly, a long-term method is required to react to the evolving dangers of climate change. The strategy is to draft risk maps by integrating climate and environmental data into epidemiological data to gain insight into the areas in NTT that are at highest risk. There are already tools in place to assist in the integration and visualization of these data layers, such as Geographic Information System (GIS) platforms, which can assist in more accurately targeting and allocating meaningful interventions and resources. These maps can help policymakers decide where resources or funds flow to where they are needed most. Incorporating climate projections into the health planning process also enables authorities to forecast future patterns of disease spread and develop adaptive strategies accordingly. Combining both these approaches helps mitigate immediate harm and simultaneously builds the capacity of communities in NTT to withstand the health consequences of climate change.