Pub Date : 2023-12-17DOI: 10.37905/euler.v11i2.23113
Steven Jansen Sinaga, Neva Satyahadewi., Hendra Perdana
Poverty refers to the condition where a person cannot meet the basic necessities based on the minimum living standards. Statistics Indonesia proxied an increase in the poverty rate in North Sumatra Province in 2021 from 8.75% to 9.01%. However, this increase is exclusive to North Sumatra Province, which has Indonesia's 3rd largest number of districts/cities. This study discussed mapping the North Sumatra Province region based on 10 poverty factor variables. The 10 variables are life expectancy, health complaints, poverty line, Gross Regional Domestic Product (GRDP), population growth rate, Expected Years of Schooling (EYS), Human Development Index (HDI), labor force participation rate, open unemployment rate, and district/city minimum wage. The Hierarchical Clustering analysis was employed to compare single, complete, and average linkage methods. The best method was determined based on the pseudo-F statistic value. 4 clusters had complete linkage methods, each of which possessed varied characteristics. Cluster 1 contains cities with the lowest poverty rate, including Medan City and Pematang Siantar City. Cluster 2 consists of cities with low poverty rates, while Cluster 3 consists of cities with high poverty rates. Cities that are included in Cluster 4 have very high poverty rates, including South Nias District and Pakpak Bharat District. The clusters present significant poverty rate gaps among North Sumatra Province regions.
{"title":"Determining the Optimum Number of Clusters in Hierarchical Clustering Using Pseudo-F","authors":"Steven Jansen Sinaga, Neva Satyahadewi., Hendra Perdana","doi":"10.37905/euler.v11i2.23113","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23113","url":null,"abstract":"Poverty refers to the condition where a person cannot meet the basic necessities based on the minimum living standards. Statistics Indonesia proxied an increase in the poverty rate in North Sumatra Province in 2021 from 8.75% to 9.01%. However, this increase is exclusive to North Sumatra Province, which has Indonesia's 3rd largest number of districts/cities. This study discussed mapping the North Sumatra Province region based on 10 poverty factor variables. The 10 variables are life expectancy, health complaints, poverty line, Gross Regional Domestic Product (GRDP), population growth rate, Expected Years of Schooling (EYS), Human Development Index (HDI), labor force participation rate, open unemployment rate, and district/city minimum wage. The Hierarchical Clustering analysis was employed to compare single, complete, and average linkage methods. The best method was determined based on the pseudo-F statistic value. 4 clusters had complete linkage methods, each of which possessed varied characteristics. Cluster 1 contains cities with the lowest poverty rate, including Medan City and Pematang Siantar City. Cluster 2 consists of cities with low poverty rates, while Cluster 3 consists of cities with high poverty rates. Cities that are included in Cluster 4 have very high poverty rates, including South Nias District and Pakpak Bharat District. The clusters present significant poverty rate gaps among North Sumatra Province regions.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139176727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-14DOI: 10.37905/euler.v11i2.23094
Maxrizal Maxrizal
The Newton-Raphson method is one of the methods to find solutions or roots of nonlinear equations. This method converges faster than other methods and is more effective in finding doubles. In this study, it will be shown that the Newton-Raphson modification uses modifications to the tangent equation. The results show that for every nth iteration, the speed difference of Newton Raphson modification is __. Furthermore, the convergence of Newton Raphson is __, and for Newton Raphson modification is __.
牛顿-拉夫逊法是寻找非线性方程的解或根的方法之一。与其他方法相比，这种方法收敛速度更快，而且在寻找倍值方面更为有效。本研究将证明牛顿-拉夫逊修正法使用了对正切方程的修正。结果表明，每迭代 n 次，牛顿-拉斐尔森修正法的速度差为__。此外，牛顿-拉斐尔森的收敛性是__，牛顿-拉斐尔森修正法的收敛性是__。
{"title":"Modifikasi Garis Singgung Untuk Mempercepat Iterasi Pada Metode Newton Raphson","authors":"Maxrizal Maxrizal","doi":"10.37905/euler.v11i2.23094","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23094","url":null,"abstract":"The Newton-Raphson method is one of the methods to find solutions or roots of nonlinear equations. This method converges faster than other methods and is more effective in finding doubles. In this study, it will be shown that the Newton-Raphson modification uses modifications to the tangent equation. The results show that for every nth iteration, the speed difference of Newton Raphson modification is __. Furthermore, the convergence of Newton Raphson is __, and for Newton Raphson modification is __.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139180177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-12DOI: 10.37905/euler.v11i2.23042
Faiqotul Mala, Muhamad Fariq Hidayat
The Human Development Index (HDI) is an indicator for measuring the level of social and economic development of a country or region. The reality is that a local-based model of autonomy is often needed because of the spatial heterogeneity that can occur due to the territory's geographical, social, cultural, or other conditions. This research aims to find spatial effects affecting HDI in West Nusa Tenggara Province. A method that can be used to accommodate is Geographically Weighter Regression (GWR). GWR analysis is the development of multiple linear regression analysis that can address territorial diversity/spatial heterogeneity so as to produce different models and predictions of parameters for each observation region. The modeling was carried out using the Gaussian Kernel Adaptive spatial weigher with an optimal bandwidth value of 27,1227 and a minimum CV value of 5,2927. The GWR model modeling resulted in 10 models for each observation location and showed that life expectancy variables, school expectance, per capita income, and average school-age significantly influenced the IPM in the West Southeast Nusa Province in 2022 with an R2 of 99.92% and a minimum AIC value of -10,0281.
{"title":"Pemodelan Indeks Pembangunan Manusia Nusa Tenggara Barat Menggunakan Geographically Weighted Regression","authors":"Faiqotul Mala, Muhamad Fariq Hidayat","doi":"10.37905/euler.v11i2.23042","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23042","url":null,"abstract":"The Human Development Index (HDI) is an indicator for measuring the level of social and economic development of a country or region. The reality is that a local-based model of autonomy is often needed because of the spatial heterogeneity that can occur due to the territory's geographical, social, cultural, or other conditions. This research aims to find spatial effects affecting HDI in West Nusa Tenggara Province. A method that can be used to accommodate is Geographically Weighter Regression (GWR). GWR analysis is the development of multiple linear regression analysis that can address territorial diversity/spatial heterogeneity so as to produce different models and predictions of parameters for each observation region. The modeling was carried out using the Gaussian Kernel Adaptive spatial weigher with an optimal bandwidth value of 27,1227 and a minimum CV value of 5,2927. The GWR model modeling resulted in 10 models for each observation location and showed that life expectancy variables, school expectance, per capita income, and average school-age significantly influenced the IPM in the West Southeast Nusa Province in 2022 with an R2 of 99.92% and a minimum AIC value of -10,0281.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139181983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The poor population is a group of people who have limited economic resources sufficient to meet their basic needs. Based on the Badan Pusat Statistik Kabupaten Blitar, the Blitar Regency has seen an increase in poor people over the past three years. This is proven by the poverty presentation from 2019 to 2021, which has increased to 8.94, 9.33, and 9.65. This research predicts the number of poor people in Blitar Regency using Brown’s Double Exponential Smoothing method. The results of calculating the best error values obtained from this research, MAD is 4.95, MSE is 49.47, and MAPE is 3.79. The error value calculation is obtained when the alpha error parameter = 0.7. The results of forecasting with Brown’s Double Exponential Smoothing method on the number of poor people in Blitar Regency for the period 2023 to 2027 is as follows: Year 2023 amounting to 100.07259, in 2024 amounting to 96.52018, in 2025 amounting to 92.96777, in 2026 amounting89.42536, and in 2027 amounting 85.86295. Based on the results obtained, it is hoped that this forecasting can help the government determine appropriate policies to improve the welfare of the people of Blitar Regency.
{"title":"Implementasi Metode Double Exponential Smoothing Brown Untuk Meramalkan Jumlah Penduduk Miskin","authors":"Zaenal Ngabidin, Ardhi Sanwidi, Ewing Rudita Arini","doi":"10.37905/euler.v11i2.23054","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23054","url":null,"abstract":"The poor population is a group of people who have limited economic resources sufficient to meet their basic needs. Based on the Badan Pusat Statistik Kabupaten Blitar, the Blitar Regency has seen an increase in poor people over the past three years. This is proven by the poverty presentation from 2019 to 2021, which has increased to 8.94, 9.33, and 9.65. This research predicts the number of poor people in Blitar Regency using Brown’s Double Exponential Smoothing method. The results of calculating the best error values obtained from this research, MAD is 4.95, MSE is 49.47, and MAPE is 3.79. The error value calculation is obtained when the alpha error parameter = 0.7. The results of forecasting with Brown’s Double Exponential Smoothing method on the number of poor people in Blitar Regency for the period 2023 to 2027 is as follows: Year 2023 amounting to 100.07259, in 2024 amounting to 96.52018, in 2025 amounting to 92.96777, in 2026 amounting89.42536, and in 2027 amounting 85.86295. Based on the results obtained, it is hoped that this forecasting can help the government determine appropriate policies to improve the welfare of the people of Blitar Regency.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139184567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-07DOI: 10.37905/euler.v11i2.23049
Seftiani Seftiani, N. Satyahadewi, N. M. Huda
Unit-linked life insurance is one of the most popular insurance products. This product connects the element of protection with investment assets in a product. Regarding option pricing, the Black Scholes model is one method that can be used. The advantage of this model is that it is a call option valuation model and is in great demand among financial associations because the option rate obtained from the calculation of this model is an accurate value. This research aims to determine the premium value of unit-linked endowment life insurance by applying the Black Scholes option pricing model. This research begins by selecting the stocks used and completing the information needed, including the insured's age, gender, insurance period, and life expectancy based on TMI in 2011. The return value and stock volatility can be calculated based on the stock data used. Furthermore, applying the Black Scholes option pricing model on customer data with male gender, age 25 years, a selected interest rate of 5.75%, and an insurance period of 5 years obtained a unit link insurance premium value of Rp123,058,412. The results showed that the Black Scholes option price model is determined by stock prices, interest rates, insurance periods, and volatility. When the longer period of insurance taken causes the premium value to be higher, and for different ages, with increasing age, the value of premiums paid will also increase.
{"title":"Penerapan Model Harga Opsi Black Scholes dalam Penentuan Premi Asuransi Jiwa Dwiguna Unit Link","authors":"Seftiani Seftiani, N. Satyahadewi, N. M. Huda","doi":"10.37905/euler.v11i2.23049","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23049","url":null,"abstract":"Unit-linked life insurance is one of the most popular insurance products. This product connects the element of protection with investment assets in a product. Regarding option pricing, the Black Scholes model is one method that can be used. The advantage of this model is that it is a call option valuation model and is in great demand among financial associations because the option rate obtained from the calculation of this model is an accurate value. This research aims to determine the premium value of unit-linked endowment life insurance by applying the Black Scholes option pricing model. This research begins by selecting the stocks used and completing the information needed, including the insured's age, gender, insurance period, and life expectancy based on TMI in 2011. The return value and stock volatility can be calculated based on the stock data used. Furthermore, applying the Black Scholes option pricing model on customer data with male gender, age 25 years, a selected interest rate of 5.75%, and an insurance period of 5 years obtained a unit link insurance premium value of Rp123,058,412. The results showed that the Black Scholes option price model is determined by stock prices, interest rates, insurance periods, and volatility. When the longer period of insurance taken causes the premium value to be higher, and for different ages, with increasing age, the value of premiums paid will also increase.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139185761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-06DOI: 10.37905/euler.v11i2.23053
Yulia Muliana, A. Abdillah, Mahsup Mahsup, S. Syaharuddin, Abdul-Lateef Olamide Ahmodu, M. M. Iddrisu
Mathematics discusses a lot about various kinds of problems that contain numbers that are classified as Higher Order Thinking Skills (HOTS). Math HOTS questions require a high level of thinking to solve the problem. Based on Bloom's theory, HOTS consists of analyzing (C4), evaluating (C5), and creating (C6). This study aims to determine the level of student errors in solving HOTS questions based on Bloom's theory. This research uses mixed method research, which is a combination of qualitative and quantitative methods, where the stages of this research include instrument development, instrument validation, data collection, data analysis and interpretation. The sample of this study used 25 students of class VIII junior high school in Mataram City. Researchers gave 10 essay questions that had been validated by material experts to students as research instruments. The results showed that students' understanding in solving HOTS problems was still lacking. For the error rate, it was found that there were no students who could solve the creating (C6) section with a percentage of 100% error, analyzing (C4) section with a percentage of 60%, evaluating (C5) 24%, applying (C3) 16%, understanding (C2) 12%, and in the remembering (C1) section there were no students who made mistakes with a percentage of 0% error. The biggest error was found in the creating part (C6), where the most mistakes were made by women with an average score of 50.55.
{"title":"Analysis of Students' Errors in Solving HOTS Problems on Algebraic Materials Based on the Complexity Level of the Problem Based on Bloom's Theory","authors":"Yulia Muliana, A. Abdillah, Mahsup Mahsup, S. Syaharuddin, Abdul-Lateef Olamide Ahmodu, M. M. Iddrisu","doi":"10.37905/euler.v11i2.23053","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23053","url":null,"abstract":"Mathematics discusses a lot about various kinds of problems that contain numbers that are classified as Higher Order Thinking Skills (HOTS). Math HOTS questions require a high level of thinking to solve the problem. Based on Bloom's theory, HOTS consists of analyzing (C4), evaluating (C5), and creating (C6). This study aims to determine the level of student errors in solving HOTS questions based on Bloom's theory. This research uses mixed method research, which is a combination of qualitative and quantitative methods, where the stages of this research include instrument development, instrument validation, data collection, data analysis and interpretation. The sample of this study used 25 students of class VIII junior high school in Mataram City. Researchers gave 10 essay questions that had been validated by material experts to students as research instruments. The results showed that students' understanding in solving HOTS problems was still lacking. For the error rate, it was found that there were no students who could solve the creating (C6) section with a percentage of 100% error, analyzing (C4) section with a percentage of 60%, evaluating (C5) 24%, applying (C3) 16%, understanding (C2) 12%, and in the remembering (C1) section there were no students who made mistakes with a percentage of 0% error. The biggest error was found in the creating part (C6), where the most mistakes were made by women with an average score of 50.55.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139186195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-12-05DOI: 10.37905/euler.v11i2.23007
N. Fadhilah, B. Prihandono., Yudhi Yudhi
UKM (Small and Medium Enterprises) X is a business that produces various types of peanut brittle. Rempeyek is suitable as a snack and is popular with children and adults. The production process of UKM X is related to the quantity of demand and availability of raw materials. Therefore, optimal production planning is needed for UKM X to meet customer demand and obtain maximum profits. The problem of production is modeled into linear programming with the method used, namely, the method of Big M. The Big-M method is used because, on the function of the barrier on the production target, there is an equation , so artificial variables must be added to its solution. In this study, a modification of the Big-M method is made, and at the completion stage, it uses iteration with the determinant algorithm of the order of two matrices. The calculation results obtained the maximum profit of UKM X in a week of Rs5.455.775 by producing 56 kg of peanuts, 20 kg of seeds, 16 kg of spinach, 23 kg of tempe, and 60 kg of shrimp to meet customer requirements and utilize the availability of raw materials. Subsequently, sensitivity analysis is performed on the target function coefficient and the right street constants of the barrier to determine how the change affects the optimal solution. The results show that the solution remains optimal when profits are in the interval obtained, but the maximum profit value changes with constant production. Based on the calculation results, raw material supplies remain optimal when the change value is within the interval obtained.
UKM（中小企业）X 是一家生产各种花生脆的企业。Rempeyek 适合作为零食，深受儿童和成人的喜爱。UKM X 的生产过程与需求量和原材料的可用性有关。因此，UKM X 需要优化生产计划，以满足客户需求并获得最大利润。使用 Big-M 方法的原因是，在生产目标的障碍函数上存在一个等式，因此必须在其解中添加人工变量。在本研究中，对 Big-M 方法进行了修改，在完成阶段使用了两个矩阵阶次的行列式算法迭代。计算结果得出，UKM X 在一周内生产 56 公斤花生、20 公斤种子、16 公斤菠菜、23 公斤豆豉和 60 公斤虾的最大利润为 5.455.775 卢比，既满足了客户要求，又利用了原材料供应。随后，对目标函数系数和障碍右街常数进行了敏感性分析，以确定变化对最优解的影响。结果表明，当利润在所获得的区间内时，方案仍然是最优的，但最大利润值会随着产量的不断变化而变化。根据计算结果，当变化值在求得的区间内时，原材料供应保持最优。
{"title":"Modifikasi Metode Big-M dan Analisis Sensitivitasnya untuk Optimasi Produksi Usaha Kecil Menengah","authors":"N. Fadhilah, B. Prihandono., Yudhi Yudhi","doi":"10.37905/euler.v11i2.23007","DOIUrl":"https://doi.org/10.37905/euler.v11i2.23007","url":null,"abstract":"UKM (Small and Medium Enterprises) X is a business that produces various types of peanut brittle. Rempeyek is suitable as a snack and is popular with children and adults. The production process of UKM X is related to the quantity of demand and availability of raw materials. Therefore, optimal production planning is needed for UKM X to meet customer demand and obtain maximum profits. The problem of production is modeled into linear programming with the method used, namely, the method of Big M. The Big-M method is used because, on the function of the barrier on the production target, there is an equation , so artificial variables must be added to its solution. In this study, a modification of the Big-M method is made, and at the completion stage, it uses iteration with the determinant algorithm of the order of two matrices. The calculation results obtained the maximum profit of UKM X in a week of Rs5.455.775 by producing 56 kg of peanuts, 20 kg of seeds, 16 kg of spinach, 23 kg of tempe, and 60 kg of shrimp to meet customer requirements and utilize the availability of raw materials. Subsequently, sensitivity analysis is performed on the target function coefficient and the right street constants of the barrier to determine how the change affects the optimal solution. The results show that the solution remains optimal when profits are in the interval obtained, but the maximum profit value changes with constant production. Based on the calculation results, raw material supplies remain optimal when the change value is within the interval obtained.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139186315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-28DOI: 10.37905/euler.v11i2.22961
Rike Marjulisa, Ayunda Putri
A definite integral that is difficult to solve analytically can be calculated using the numerical integration methods. The midpoint rule is a prominent rule for approximating definite integrals. This article discusses a version of the quartet midpoint rule that includes the derivative of the arithmetic mean . The proposed rule increases precision over the previous rules. Furthermore, the error term is obtained by using the concept of precision between quadrature and exact values. Finally, the proposed rule is more effective than the present rule, according to numerical simulation results.
{"title":"Arithmetic Mean Derivative-Based Quartet Midpoint Rule","authors":"Rike Marjulisa, Ayunda Putri","doi":"10.37905/euler.v11i2.22961","DOIUrl":"https://doi.org/10.37905/euler.v11i2.22961","url":null,"abstract":"A definite integral that is difficult to solve analytically can be calculated using the numerical integration methods. The midpoint rule is a prominent rule for approximating definite integrals. This article discusses a version of the quartet midpoint rule that includes the derivative of the arithmetic mean . The proposed rule increases precision over the previous rules. Furthermore, the error term is obtained by using the concept of precision between quadrature and exact values. Finally, the proposed rule is more effective than the present rule, according to numerical simulation results.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139221247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-28DOI: 10.37905/euler.v11i2.22761
Ririn Febriyanti, B. Prihandono., M. Kiftiah.
Hepatitis B is an infection of the liver that can cause liver cirrhosis. Liver cirrhosis can occur due to the formation of scar tissue in individuals who have prolonged hepatitis B. Transmission of hepatitis B can occur in two ways, namely horizontal and vertical. In this research, this problem is modeled in a mathematical model using the SIRC model, where the population is grouped into four sub-populations, namely susceptible (S), infected (I), cured or immune due to vaccination (R) and cirrhosis. liver (C). From the analysis, two equilibrium points were obtained, namely the disease-free equilibrium point the endemic equilibrium point The basic reproduction number is obtained using the Next Generation Matrix. The analysis results show that if , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if , this means that hepatitis B transmission in liver cirrhosis is influenced by contact between susceptible and infectious individuals. To support the results of the analytical analysis, numerical simulations are provided to describe the behavior of the SIRC model.
{"title":"Analisis Dinamik Model SIRC pada Transmisi Hepatitis B dengan Sirosis Hati","authors":"Ririn Febriyanti, B. Prihandono., M. Kiftiah.","doi":"10.37905/euler.v11i2.22761","DOIUrl":"https://doi.org/10.37905/euler.v11i2.22761","url":null,"abstract":"Hepatitis B is an infection of the liver that can cause liver cirrhosis. Liver cirrhosis can occur due to the formation of scar tissue in individuals who have prolonged hepatitis B. Transmission of hepatitis B can occur in two ways, namely horizontal and vertical. In this research, this problem is modeled in a mathematical model using the SIRC model, where the population is grouped into four sub-populations, namely susceptible (S), infected (I), cured or immune due to vaccination (R) and cirrhosis. liver (C). From the analysis, two equilibrium points were obtained, namely the disease-free equilibrium point the endemic equilibrium point The basic reproduction number is obtained using the Next Generation Matrix. The analysis results show that if , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if , then the disease-free equilibrium point is locally asymptotically stable, which means that hepatitis B transmission in liver cirrhosis does not spread. Meanwhile, if , this means that hepatitis B transmission in liver cirrhosis is influenced by contact between susceptible and infectious individuals. To support the results of the analytical analysis, numerical simulations are provided to describe the behavior of the SIRC model.","PeriodicalId":504964,"journal":{"name":"Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139216400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-24DOI: 10.37905/euler.v11i2.21169
Theodora Tantri Trisnawati, Sherli Yurinanda, Wardi Syafmen, C. Multahadah
PT. Rezeki Surya Gasindo is a company that uses websites to store important company data, one of which is customer personal data. PT. Rezeki Surya Gasindo’s website is protected by a login system. However, a login system alone is not enough to protect the data stored on the website from cases of data theft by third parties. One solution to this problem is to encrypt the website's Uniform Resource Locator (URL) to increase the security level of data stored on the website. In this research, the Rivest-Shamir-Adleman (RSA) algorithm is used for the encryption process. The aim of this research is to determine the process of applying the Rivest-Shamir-Adleman (RSA) algorithm to the Uniform Resource Locator (URL) encryption of the PT. Surya Gasindo's website. The success of applying encryption with the RSA algorithm is observed from changes in the get parameter value that appears in the URL bar. The encrypted message is the customer, the get parameter in the Customer menu, which contains the consumer's personal data. By choosing two large prime numbers, namely 151 and 173, and taking one of the public keys/encryption keys, namely 16379, the result is that the get parameter in the URL bar has changed to the code string 5a9cb05811aa6e4c. The RSA algorithm has been successfully applied to the website URL.
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