Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6, 4518-4528 2024 Publisher: Learning Gate DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate © 2024 by the authors; licensee Learning Gate * Correspondence: mutammimul@unimal.ac.id Implementation of ward's agglomerative hierarchical clustering model to detect pulmonary tuberculosis endemic areas in Aceh Utara regency Mutammimul Ula1*, Mauliza2, Ar Razi3, Ilham Sahputra4, Muhammad Abdullah Ali5, Yumna Rilasmi Said6 1,4,5,6Department of Information Systems, Faculty of Engineering, Universitas Malikussaleh, Aceh, Indonesia. mutammimul@unimal.ac.id (M.U.) 2Department of Medical Education, Faculty of Medicine, Universitas Malikussaleh, Aceh, Indonesia. 3Department of Informatics Engineering, Faculty of Engineering, Universitas Malikussaleh, Aceh, Indonesia. Abstract: This study aims to detect pulmonary Tuberculosis (TB) endemic areas in Aceh Utara Regency based on altitude, population density, and the number of TB cases. The Agglomerative Hierarchical Clustering (AHC) algorithm was used to cluster 27 subdistricts, each measured by these three factors. The clustering results divided the subdistricts into three main clusters with distinct characteristics. Cluster 1 consists of subdistricts with low altitude, high population density, and relatively high numbers of TB cases, identifying this area as having the highest risk of TB endemicity. Cluster 2 includes areas with moderate population density and TB case numbers, while Cluster 3 consists of subdistricts at higher altitudes with fewer TB cases. The clustering results were evaluated using three key metrics: Silhouette Score, Davies-Bouldin Index, and Dunn Index, which indicated that the clustering model performed well, although some subdistricts were positioned near the cluster boundaries. This research provides valuable information for health authorities to prioritize interventions and allocate resources to areas most in need of TB management. Keywords: AHC, Cluster evaluation, Clustering, Pulmonary TB, Ward. 1. Introduction Pulmonary Tuberculosis (TB) is an infectious disease that remains a public health issue in Indonesia [1]. According to the World Health Organization (WHO), Indonesia is one of the countries with the highest TB burden in the world [2], with Aceh Utara being one of the regions with high prevalence [3]. This disease is transmitted through the air, and environmental and socioeconomic factors can contribute to its spread [4] [5]. In this context, factors such as altitude, population density, and the number of cases are crucial to consider when detecting and mapping pulmonary TB endemic areas [6] [7]. The size of an area is related to accessibility and the distribution of health resources, while altitude can influence disease spread patterns through changes in climate and habitat [8]. Population density is a critical factor that can increase the risk of TB transmission, as frequent interactions among individuals in densely populated areas can heighten the likelihood of infection [9] [10]. Therefore, understanding how these three factors interact can assist in detecting areas at high risk for pulmonary TB [11] [12]. Clustering is an effective technique for grouping data based on specific characteristics [13] [14]. One commonly used clustering method is the Agglomerative Hierarchical Clustering (AHC) algorithm [15]. This method can divide data into interrelated clusters, allowing for the identification of patterns that may not be evident in traditional analysis [16] [15]. This study aims to explore and analyze existing data using the AHC algorithm to identify clusters of pulmonary TB endemic areas in Aceh Utara Regency, [17], based on altitude, population density, and the number of cases [18]. The results of this study are expected to provide useful information for policymakers in designing more effective and targeted interventions to combat pulmonary TB in the region. 4519 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate 2. Literature Review 2.1. Pulmonary Tuberculosis and Its Impact in Indonesia Pulmonary Tuberculosis (TB) is an infection caused by the Mycobacterium tuberculosis bacteria, which attacks the respiratory system and can lead to death if not properly treated [18]. TB remains one of the leading causes of morbidity and mortality worldwide, including in Indonesia, which ranks second after India in the number of TB cases, with approximately 845,000 new cases diagnosed in 2022 [2]. The high prevalence of pulmonary TB in Indonesia is influenced by various factors, including population density and access to healthcare services [19]. dditionally, environmental factors such as the size of the area and altitude, as well as demographic factors like population density, significantly affect the spread of pulmonary TB [20]. A deep understanding of these factors is crucial for identifying endemic TB areas and focusing public health interventions [2] [20]. 2.2. Factors of Population Density, Area Size, and Altitude in the Spread of Pulmonary TB Research shows that areas with high population density have a greater risk for the spread of pulmonary TB [21], as this condition allows for rapid disease transmission, especially in urban areas that often face space limitations and lower access to healthcare services [22]. Increased population density is directly related to a higher prevalence of pulmonary TB, particularly in areas that receive less attention regarding health interventions [23] [24]. This factor is crucial in the spread of TB because densely populated areas typically have more social interactions, which increases the likelihood of transmission [20]. Studies in various countries have also shown that increased population density is directly related to a rise in TB cases [20]. Additionally, the size of an area is often associated with the spread of diseases, including TB. Some studies have found that larger areas carry a higher risk of disease transmission, especially in regions with limited access to healthcare services [25] [26]. Altitude can also influence TB prevalence, where lower-altitude regions tend to have conditions more conducive to TB transmission due to higher temperatures and humidity [27]. 2.3. Clustering Algorithms in Epidemiological Analysis The Agglomerative Hierarchical Clustering (AHC) algorithm is a method frequently used to group data based on similarities or distances between data points [27]. This method is effective in identifying patterns and structures within complex data [28]. The advantage of AHC lies in its ability to produce hierarchical representations that provide a deeper understanding of the cluster structures formed [15]. In the context of pulmonary TB, AHC can assist in identifying areas at high risk based on demographic and epidemiological factors. Several previous studies have applied AHC to analyze health data, including mapping the spread of pulmonary TB in various regions [29]. In the field of epidemiology, clustering can be used to identify disease spread patterns, including pulmonary TB [30]. In this research context, AHC can be utilized to cluster districts in North Aceh based on altitude, population density, and the number of cases, thus facilitating the identification of TB endemic areas [31]. 2.4. Application of AHC in Pulmonary TB Health Research The application of clustering methods in the health sector has proven successful in identifying areas that require further intervention [30]. A study shows that clustering analysis can aid in planning more efficient disease control strategies [28]. Therefore, this research aims to apply AHC to detect endemic areas of pulmonary TB in North Aceh Regency, considering factors such as altitude, population density, and the number of cases. The application of AHC in pulmonary TB health research shows promising results [30]. For instance, in a study, AHC was used to identify clusters of areas with high prevalence of respiratory diseases, including pulmonary TB [28]. This research highlights the importance of using demographic and health data to better understand the spread of TB and to focus health interventions in at-risk areas. In Indonesia, the application of clustering algorithms in the context of pulmonary TB is still limited. However, by utilizing existing data, mapping endemic areas of pulmonary TB can enhance the 4520 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate effectiveness of health programs [32], especially in terms of resource allocation and the development of more targeted prevention strategies [33]. Therefore, this research aims to apply AHC to detect endemic areas of pulmonary TB in North Aceh Regency, considering population density, altitude, and the number of cases as the main variables. 2.5. Comparison with Other Clustering Algorithms In addition to AHC, various other clustering algorithms such as K-Means and DBSCAN have been applied for mapping endemic areas of infectious diseases [34]. KK-Means groups data based on a predetermined number of clusters and is effective for data with a clear distribution, while DBSCAN can identify irregularly shaped clusters and handle outliers more effectively [35]. However, AHC has the advantage of hierarchical analysis, which can identify complex relationships between areas that may not be detected by other algorithms. Therefore, AHC was chosen in this study to map TB endemic areas based on population density and mortality rates, with the hope of providing deeper insights for public health interventions. 3. Methods 3.1. Research Design This study employs a quantitative research design with a descriptive approach. The aim is to analyze and identify endemic areas of pulmonary TB in Aceh Utara Regency based on the factors of altitude, population density, and the number of cases using the Agglomerative Hierarchical Clustering (AHC) algorithm. Figure 1 illustrates the stages of the research process. Figure 1. Research stages. 3.2. Data and Data Sources The data used in this study includes all districts in North Aceh Regency, totaling 27 districts. The data utilized in this research comprises: 1. Altitude (meters): Altitude data is obtained from publications issued by the North Aceh BPS (Central Bureau of Statistics). 2. Population Density (people/km²): This data is sourced from population census data published by the Aceh Utara BPS. 3. Number of Cases: Data is collected from Cut Meutia Hospital. 4521 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate 3.3. Data Analysis Data analysis is conducted in several steps: 1. Data Preprocessing: The obtained data will be cleaned of missing values and standardized to ensure it is on the same scale [36]. The following is the formula used: 𝑍 = 𝑋 − 𝜇 𝜎 (1) 𝑍 is the standardized data value (z-score), 𝑋 is the original data value, 𝜇 is the mean of all data values, and 𝜎 is the standard deviation of the data. 2. Application of the AHC Algorithm: AHC is applied to cluster the districts based on the four factors under study. The clustering process is carried out with the following steps: a) Creating a Distance Matrix: Calculate the distance between districts using the Euclidean method. The formula is as follows: 𝑑(𝑝, 𝑞) = √∑(𝑞1 − 𝑝1)2 (2) 𝑛 𝑖=1 𝑑(𝑝, 𝑞) is the Euclidean distance between two points 𝑝 and 𝑞, 𝑝𝑖 and 𝑞𝑖 are the coordinates of points 𝑝 and 𝑞 in the 𝑖-th dimension, b) Clustering Process: Using the agglomerative method to hierarchically group the data. Each district will be treated as an individual cluster and then merged based on their proximity in distance [33]. c) Determination of the Number of Clusters: The number of clusters will be determined using a dendrogram to visualize the clustering results and select the appropriate cutoff point. 3. The clustering results will be visualized using a dendrogram to facilitate understanding of the structure of the formed clusters. 4. Cluster Evaluation: The evaluation of the clustering results is conducted using the Silhouette Score, Davies-Bouldin Index, and Dunn Index metrics to assess the quality of the formed clusters (Rousseeuw, 1987). Below are some formulas used: a) Silhouette Score 𝑆(𝑖) = 𝑏(𝑖) − 𝑎(𝑖) max (𝑎(𝑖), 𝑏(𝑖)) (3) 𝑆(𝑖) is the Silhouette value for the 𝑖-th data point, 𝑎(𝑖) is the average distance from the 𝑖-th data point to all other data points in the same cluster (internal cluster cohesion), and 𝑏(𝑖) is the average distance from the 𝑖-th data point to all points in the nearest cluster that is not its own (distance to the nearest cluster). b) Davies-Bouldin Index 𝐷𝐵𝐼 = 1 𝑛 ∑ 𝑚𝑎𝑥𝑖≠𝑖 (𝑠𝑖 + 𝑠𝑗) 𝑑𝑖,𝑗 (4) 𝑛 𝑖=1 𝑛 represents the total number of clusters, 𝑠𝑖 a is the spread or average distance between the data points in cluster 𝑖 and the centroid of cluster 𝑖 (intra-cluster distance), and, 𝑑𝑖,𝑗 is the distance between the centroids of cluster 𝑖 and cluster 𝑗 (inter-cluster distance). The term 𝑚𝑎𝑥𝑖≠𝑖 (𝑠𝑖+𝑠𝑗) 𝑑𝑖,𝑗 calculates the worst-case ratio between clusters 𝑖 and 𝑗, and this value is maximized across all cluster pairs to assess how well-separated the clusters are. c) Dunn Index 4522 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate 𝐷 = 𝑚𝑖𝑛1≤𝑖<𝑗≤𝑘 𝑑(𝐶𝑖, 𝐶𝑗) 𝑚𝑎𝑥1≤𝑙≤𝑘 ∆(𝐶𝑙) (5) 𝑑(𝐶𝑖, 𝐶𝑗) represents the minimum distance between two clusters 𝐶𝑖 and 𝐶𝑗 (the closest distance between points in these two clusters). ∆(𝐶𝑙) is the spread (diameter) of cluster (𝐶𝑙), and 𝑘 which measures the maximum distance between any two points within the same cluster. 5. Interpretation of Results: Each cluster formed will be analyzed to identify which districts are classified as endemic areas for pulmonary TB. The assessment criteria include high population density and a significant number of deaths due to pulmonary TB.. 4. Result and Discussion 4.1. Data Collection Results The data used in this study covers 27 sub-districts across various regions. Each sub-district was measured based on three main features: Elevation (meters above sea level), Population Density (number of residents per km²), and the Number of TB Cases. These factors were selected as they can influence the spread of infectious diseases such as TB, where elevation affects environmental conditions, population density influences transmission potential, and the number of cases serves as an indicator of endemic levels. The data collection results show significant variation among the sub-districts, with elevation ranging from 5 meters to 362 meters, population density from 22 to 1,188 people/km², and TB cases ranging from 2 to 32 cases per sub-district. Table 1 presents the detailed data collected in this study. 4.2. Data Normalization Before the clustering process is carried out, the data is normalized using the Standardization method to ensure that each feature has a uniform scale. This is important because each feature has different units (meters, people/km², and case numbers), and without normalization, features with a larger scale, such as elevation, could dominate the clustering process. Normalization is done by subtracting the mean from each feature and dividing it by the standard deviation, resulting in each feature having a mean of zero and a standard deviation of one. The normalization results allow the clustering algorithm to treat all features equally during the cluster formation process. 4523 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate Table 1. Dataset of pulmonary TB cases in Aceh Utara regency. NO District Elevation (Meters above sea level) Population density (People/km ²) Number of cases No District Elevation (Meters above sea level) Population density (People/km²) Number of cases 1 Baktiya 10 249 17 15 Meurah Mulia 25 110 9 2 Lhoksukon 7 212 27 16 Nibong 12 251 9 3 Samudera 19 655 19 17 Nisam 25 181 11 4 Seunuddon 9 263 21 18 Pirak Timu 11 134 12 5 Syamtalira Aron 8 708 17 19 Syamtalira Bayu 7 296 11 6 Tanah Jambo Aye 9 276 32 20 Tanah Pasir 6 497 6 7 Tanah Luas 13 861 25 21 Cot Girek 151 109 10 8 Dewantara 8 1188 9 22 Geuredong Pase 195 22 2 9 Muara Batu 7 857 10 23 Kuta Makmur 168 187 4 10 Baktiya Barat 8 239 8 24 Nisam Antara 362 166 4 11 Banda Baro 13 199 3 25 Paya Bakong 113 38 13 12 Langkahan 64 154 5 26 Sawang 198 104 6 13 Lapang 6 460 2 27 Simpang Kramat 165 138 3 14 Matang Kuli 5 345 5 4524 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate Table 2. Normalized dataset. No District Elevation (Meters above sea level) Population density (People/km² ) Number of cases No District Elevation (Meters above sea level) Population Density (People/km ²) Number of cases 1 Baktiya -0.5705 -0.28531 0.749533 15 Meurah Mulia -0.39986 -0.77739 -0.2687 2 Lhoksukon -0.60463 -0.4163 2.022325 16 Nibong -0.54775 -0.27823 -0.2687 3 Samudera -0.46812 1.151997 1.004092 17 Nisam -0.39986 -0.52604 -0.01414 4 Seunuddon -0.58188 -0.23575 1.25865 18 Pirak Timu -0.55913 -0.69243 0.113137 5 Syamtalira Aron -0.59326 1.339626 0.749533 19 Syamtalira Bayu -0.60463 -0.11892 -0.01414 6 Tanah Jambo Aye -0.58188 -0.18973 2.658721 20 Tanah Pasir -0.61601 0.59265 -0.65054 7 Tanah Luas -0.53638 1.881272 1.767767 21 Cot Girek 1.033566 -0.78093 -0.14142 8 Dewantara -0.59326 3.038907 -0.2687 22 Geuredong Pase 1.534127 -1.08893 -1.15966 9 Muara Batu -0.60463 1.867111 -0.14142 23 Kuta Makmur 1.226965 -0.5048 -0.9051 10 Baktiya Barat -0.59326 -0.32071 -0.39598 24 Nisam Antara 3.433985 -0.57915 -0.9051 11 Banda Baro -0.53638 -0.46232 -1.03238 25 Paya Bakong 0.601263 -1.03229 0.240416 12 Langkahan 0.04382 -0.62163 -0.77782 26 Sawang 1.568257 -0.79864 -0.65054 13 Lapang -0.61601 0.461664 -1.15966 27 Simpang Kramat 1.192836 -0.67827 -1.03238 14 Matang Kuli -0.62739 0.054545 -0.77782 4525 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate 4.3. Results of Regional Clusters After the data was normalized, the Agglomerative Hierarchical Clustering (AHC) algorithm was applied to detect endemic regions of tuberculosis (TB). This algorithm uses Ward's linkage method to minimize variance within clusters. The results of the clustering are shown in the following figure: Figure 2. Dendrogram of the clustering results for the regions. Based on the clustering results, the sub-districts are divided into three main clusters, with the members of each cluster shown in Table 3. Table 3. Clustering results of regions. Cluster District 1 Baktiya, Lhoksukon, Samudera, Seunuddon, Syamtalira Aron, Tanah Jambo Aye, Tanah Luas, Dewantara, Muara Batu. 2 Baktiya Barat, Banda Baro, Langkahan, Lapang, Matang Kuli, Meurah Mulia, Nibong, Nisam, Pirak Timu, Syamtalira Bayu, Tanah Pasir. 3 Cot Girek, Geuredong Pase, Kuta Makmur, Nisam Antara, Paya Bakong, Sawang, Simpang Kramat Each cluster has distinct characteristics, as described below: 4526 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate 1) Cluster 1: Areas with low elevation (5-19 meters), medium to high population density (249-1188 people/km²), and a relatively high number of TB cases (9-32 cases). This cluster is dominated by areas at high risk of transmission due to the dense population. 2) Cluster 2: Districts with low to moderate elevation (5-25 meters), lower population density (110-497 people/km²), and a varying number of TB cases, but generally lower compared to Cluster 1 (2-11 cases). These areas exhibit more moderate environmental and demographic conditions. 3) Cluster 3: Districts with higher elevation (113-362 meters), varying population density, and a relatively low number of TB cases (2-13 cases). Areas in this cluster tend to have more challenging environmental conditions, which may influence the rate of disease transmission. 4.4. Evaluation of Clusters The quality evaluation of the clustering results is conducted using three main metrics: Silhouette Score, Davies-Bouldin Index (DBI), and Dunn Index. 1) Silhouette Score: The obtained value is 0.397, which indicates that most districts are clustered well; however, some districts are on the border between clusters. This value suggests a fairly good separation of clusters but not perfect, where some districts could potentially be grouped more optimally. 2) Davies-Bouldin Index (DBI): The DBI value is 0.879, indicating that the formed clusters are compact and separated from each other. A DBI value close to 1 shows fairly distinct clusters, with moderate intra-cluster variation. 3) Dunn Index: The generated Dunn Index is 0.439, which indicates that the distance between clusters is still quite good, although it could be improved to make the clusters more compact and further separated from each other. Overall, the evaluation results indicate that the formed clusters are quite good, although there are still some districts that are on the borders between clusters and have characteristics similar to other clusters. 4.5. Interpretation of Results Based on the results of clustering and evaluation, Cluster 1 can be considered as the area with the highest risk of TB endemicity, characterized by a high population density and a relatively larger number of cases. Areas in this cluster need more attention in efforts to prevent and manage TB due to the high potential for transmission. Cluster 2 represents districts with a moderate endemic risk, where the population density is lower than in Cluster 1, but the number of cases still requires monitoring. This area may have environmental and social factors that influence the disease's transmission rate. Meanwhile, Cluster 3 consists of areas with higher elevations and a lower number of TB cases. This suggests that physical environments, such as altitude and greater distances from population centers, may play a role in limiting disease spread. Efforts in this cluster could focus on prevention to avoid an increase in cases. 5. Conclusion Based on the clustering results using the Agglomerative Hierarchical Clustering (AHC) algorithm, districts in North Aceh Regency are divided into three main clusters based on the features of elevation, population density, and the number of TB cases. 1. This finding provides guidance in identifying areas with different levels of TB endemic risk. Cluster 1 includes districts with high population density and a larger number of TB cases, indicating areas with a faster potential for disease spread that require prioritized health interventions. Cluster 2 consists of areas with moderate demographic and epidemiological characteristics, where the number of TB cases is relatively controlled, although there is still a potential for transmission that should be monitored. Cluster 3 includes areas with higher elevations and fewer cases, suggesting that geographical factors such as altitude may play a role in limiting the spread of TB. 4527 Edelweiss Applied Science and Technology ISSN: 2576-8484 Vol. 8, No. 6: 4518-2528, 2024 DOI: 10.55214/25768484.v8i6.2984 © 2024 by the authors; licensee Learning Gate 2. The evaluation of clustering results with a Silhouette Score of 0.397, Davies-Bouldin Index of 0.879, and Dunn Index of 0.439 indicates that the clustering model has produced fairly good clusters, although there is room for improvement in separating some districts that are on the border between clusters. 3. Overall, this research provides important insights into detecting areas with a higher risk of TB endemicity, allowing prevention and management strategies to be focused on the areas most in need. This clustering approach can also help health authorities allocate resources more efficiently and effectively. Copyright: © 2024 by the authors. 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