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SEIR MODELING OF TUBERCULOSIS TRANSMISSION WITH VACCINATION: ESTIMATING THE MINIMUM COVERAGE REQUIRED FOR ELIMINATION IN NORTH SUMATERA Nasution, Hamidah; Mulyono, Mulyono; Cyntia S., Maria; Ahyaningsih, Faiz; Nofertinus Zai, Fidelis
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 4 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss4pp3073-3086

Abstract

Tuberculosis (TB) remains one of the most significant public health challenges in Indonesia, particularly in North Sumatra Province, which records a relatively high prevalence rate. e–Exposed–Infectious–Recovered) A framework to analyze TB's transmission dynamics and evaluate vaccination's effectiveness as an intervention strategy. The primary objective of this research is to estimate the minimum vaccination coverage required to eliminate TB from the population. The model was built by incorporating vaccination rate parameters into the SEIR mathematical model and applied using regional epidemiological data obtained from the North Sumatra Central Bureau of Statistics. A deterministic approach is employed to simulate the system and derive the basic reproduction number ( ), which serves as an indicator of disease persistence across various levels of vaccination coverage. The results of numerical simulations performed using 4th-Order Runge Kutta indicate the existence of a critical vaccination threshold required to reduce below the one-condition that theoretically represents the possibility of disease elimination from the population. These findings provide a quantitative basis for formulating more targeted, data-driven vaccination policies. Calculations based on real-world data reveal that the current R₀ value in North Sumatra remains above one ( ), suggesting that TB continues to pose a risk of remaining endemic. Simulations were also conducted by varying the vaccination coverage while assuming a constant transmission rate, indicating that a minimum of 87.5% vaccination coverage is required to suppress R₀ below the critical threshold. This study underscores the importance of employing mathematical modeling as a decision-support tool in public health policy. The findings deepen the understanding of TB transmission dynamics and offer a robust quantitative foundation for setting vaccination targets for disease elimination in endemic areas such as North Sumatra.
Analisis Strategi Optimasi Menggunakan Teori Permainan Dan Markov Chain Terhadap Persaingan E-Wallet Nuhrul Huda, Ella; Nasution, Hamidah; Husein, Ismail
Journal of Comprehensive Science Vol. 2 No. 7 (2023): Journal of Comprehensive Science (JCS)
Publisher : Green Publisher Indonesia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59188/jcs.v2i7.449

Abstract

Persaingan dunia digital semakin meningkat dengan pemanfaatannya dalam kegiatan masyarakat salah satunya adalah e-wallet. Penggunaannya yang cukup mudah dan efesien menyebabkan banyak masyarakat meminatinya. Penelitian ini bertujuan untuk menganalisis strategi persaingan e-wallet yang optimal menggunakan metode matematika yaitu Teori Permainan dan Rantai Markov. Hasil penelitian yang diperoleh menunjukkan persaingan antara GoPay dan OVO menghasilkan strategi optimal yang sama yaitu promosi, keamanan dan praktis. Pada persaingan Dana dan OVO strategi optimal Dana adalah promosi dan keamanan. Sedangkan strategi OVO adalah keamanan dan praktis. Pada persaingan Dana dan GoPay strategi optimal Dana yaitu promosi, tempat, dan praktis. Sedangkan strategi GoPay adalah produk, promosi, dan tempat. Perpindahan merek menggunakan Markov Chain didapat probabilitas GoPay 0,486, OVO 0,303, dan Dana 0,212.
Analysis Of Multi Item Raw Material Inventory Supply Using The Economic Order Quantity Method Anidah, Anidah; Nasution, Hamidah; Widyasari, Rina
ZERO: Jurnal Sains, Matematika dan Terapan Vol 4, No 1 (2020): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v4i1.8415

Abstract

Raw material inventory control has a positive impact to support the smooth production process in increasing company profits, one of which is the production of chicken feed at PT. Mabar Feed Indonesia. This study aims to determine the economic order quantity of multi-item chicken feed raw material inventory, and to compare the control of multi-item chicken feed raw material inventory used by companies with the control of multi item chicken feed inventory using the EOQ method. In this study to analyze the data first used the normality test data with the Lilliefors test where the data is normally distributed. The total cost of raw material inventory according to PT Mabar Feed Indonesia is Rp.   the cost is greater than the cost obtained by the EOQ method, which is Rp.   and savings can be made of  Rp.   of the cost of raw material inventory according to PT. Mabar Feed Indonesia.
Application of Graph Coloring on Nurse Work Scheduling at H. Adam Malik Hospital Medan Using the Tabu Search Algorithm Ananda, Rizky; Indra, Zulfahmi; Nasution, Hamidah
ZERO: Jurnal Sains, Matematika dan Terapan Vol 6, No 1 (2022): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v6i1.12451

Abstract

Complex problems that usually occur in every hospital, one of which is scheduling with so many aspects, for example: the number of nurses, the distribution of nurse shifts, time off or leave and others. With the manual method that is still used in compiling the nurse's work schedule, it makes it difficult for an irregular and regular schedule. In solving the scheduling problem, the graph coloring method can be used. This scheduling problem can be solved by graph coloring. One solution to solve the problem of concluding graphs in scheduling is the Tabu Search Algorithm. A method that works as an effective problem solving method in finding the best solution to a problem. A method is used to solve the problem by making a representation in the form of a graph where the nurse is a node and grouping nurses as an edge by implementing the graph coloring into the Tabu Search Algorithm.
DETERMINATION OF DOMINANT SIDE CONTRACTION NUMBERS IN BANANA TREE AND FIRECRACKER GRAPES Simanungkalit, Devi Febriany; Mulyono, Mulyono; Nasution, Hamidah
ZERO: Jurnal Sains, Matematika dan Terapan Vol 7, No 2 (2023): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v7i2.17770

Abstract

This research aims to determine the pattern of dominance side contraction numbers in banana tree graphs and fireworks graphs. Banana tree graph Bn,,k is  a graph obtained by connecting one leaf from each n-copies  of a k star graph with one vertex that is different from all the star graphs. The fireworks graph  is a tree that is similar to the caterpillar graph, the difference lies in the backbone node n which is connected to the earring node k from the caterpillar graph. The dominating number is denoted by γ ( G ) is the smallest cardinality of a dominating set. Domination set The minimum is a dominating set from which no points can be removed without changing its dominance. Domination contraction number of a graph ctγ ( G ) is defined as the minimum number of edges that must be contracted to reduce the dominance number .
OPTIMIZING RAW MATERIAL INVENTORY USING ECONOMIC ORDER QUANTITY (EOQ) METHOD IN BOMBAY BAKERY Hannum, Syaripah; Ahyaningsih, Faiz; Nasution, Hamidah
ZERO: Jurnal Sains, Matematika dan Terapan Vol 7, No 1 (2023): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v7i1.17562

Abstract

Bombay Bakery is a bakery that operates in the field of bread production. Various raw materials used in bread production include wheat flour, butter, sugar, bread improver, eggs and so on. This research aims to determine the optimal order quantity of raw materials each time an order or purchase is made, for the Reorder Point and for the total cost of raw material inventory using the Economic Order Quantity (EOQ). Data collection techniques were carried out by means of library studies and field research. The data analysis technique used is quantitative data analysis technique. Based on perhi analysisThe profit was obtained by ordering or purchasing 659 Kg of raw materials for wheat flour, 37 Kg of butter, 102 Kg of sugar, 3 Kg of bread improver, and 11 eggs with a reorder point for wheat flour raw materials of 501 Kg, 24 Kg of butter, 65 Kg of sugar, 1 Kg of bread leaven, and 8 pieces of eggs. With total costs using company policy of IDR 22,740,233.- while using the Economic Order Quantity (EOQ) model it is IDR 12,761,888.-  so that using the Economic Order Quantity (EOQ) model is more effective in saving raw material inventory costs
IMPLEMENTATION OF THE DOUBLE EXPONENTIAL SMOOTHING (DES) METHOD TO FORECET THE CONSUMER PRICE INDEX (CPI) IN MEDAN CITY Hutagalung, Goklas; Nasution, Hamidah
ZERO: Jurnal Sains, Matematika dan Terapan Vol 6, No 1 (2022): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v6i1.12455

Abstract

The Central Statistics Agency (BPS) as a non-ministerial government agency has the task of providing data needs for the government and the public obtained through censuses and surveys conducted by BPS itself and also from other government departments or agencies as secondary data.  The problem that occurs at BPS is   the field of inflation, one of which is in the field of the consumer price index, which experiences price fluctuations which have an impact on the economy. Forecasting is an important tool used for effective and efficient planning, therefore, forecasting is needed to predict various events that will occur in the future. One of the methods used for forecasting is the linear Double Exponential Smoothing (DES) method from Brown, this method basically uses past data which is smoothed by exponen- tially weighting the older observation values or newer values and the data used shows trend pattern. Trend is a smoothed estimate of the average growth at the end of the period. In this study, the best parameter α for forecasting the consumer price index in the city of Medan is α= 0,8 with a MAPE percentage of 0,0223. And the results of the consumer price index forecast in the city of Medan in 2022-2023 show an increase every month.
Sistem Pakar Diagnosa Penyakit Ginjal Menggunakan Metode Dempster Shafer Di Rsud Pirngadi Medan Parapak, R Putri Angela; Kana Saputra S; Nasution, Hamidah; Indra, Zulfahmi; Taufik, Insan
Innovative: Journal Of Social Science Research Vol. 4 No. 5 (2024): Innovative: Journal Of Social Science Research
Publisher : Universitas Pahlawan Tuanku Tambusai

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31004/innovative.v4i5.15895

Abstract

Dalam era modern yang dipenuhi dengan kemajuan teknologi komputerisasi, perkembangan teknologi informasi terjadi dengan kecepatan yang luar biasa dan memiliki dampak yang signifikan dalam berbagai aspek kehidupan manusia. Dalam konteks ini, penting untuk diakui bahwa penyakit ginjal merupakan salah satu masalah kesehatan yang perlu mendapatkan perhatian serius dari masyarakat. Sayangnya, penyakit ini seringkali sulit dideteksi secara dini dan dapat mengancam nyawa seseorang jika tidak ditangani dengan tepat. Dalam situasi di mana kesadaran akan kesehatan seringkali rendah, terdapat kebutuhan yang mendesak untuk mengembangkan solusi yang dapat membantu meningkatkan deteksi dini dan diagnosis penyakit ginjal. Salah satu solusi yang inovatif adalah dengan memanfaatkan teknologi informasi dalam bentuk aplikasi sistem pakar. Melalui pendekatan ini, penulis merancang sebuah aplikasi sistem pakar yang bertujuan untuk mendeteksi penyakit ginjal akut dan kronis. Aplikasi ini dibangun dengan menggunakan metode Dempster-Shafer, sebuah teknik yang mampu menggabungkan data dari berbagai sumber untuk menghasilkan estimasi yang lebih akurat. Dengan menggunakan bahasa pemrograman PHP, HTML, dan SQL Server, aplikasi ini mampu mengumpulkan gejala yang dilaporkan oleh pengguna dan menganalisisnya untuk memberikan diagnosis yang lebih tepat. Tidak hanya memberikan diagnosis, aplikasi ini juga memberikan informasi tentang tingkat kepercayaan terhadap kemungkinan penyakit ginjal yang diderita oleh pengguna. Dengan memberikan informasi yang komprehensif dan akurat, aplikasi ini diharapkan dapat membantu pengguna dalam mengidentifikasi penyakit ginjal yang mungkin dialami dan memberikan informasi yang berguna untuk langkah-langkah pengobatan selanjutnya. Dengan demikian, aplikasi sistem pakar ini tidak hanya bertujuan untuk meningkatkan kesadaran akan pentingnya deteksi dini terhadap penyakit ginjal, tetapi juga untuk memberikan solusi yang konkret dan terukur dalam menangani masalah kesehatan ini.
Dynamic analysis of SEIR model for Covid-19 spread in Medan Sihaloho, Ruth Salisa; Nasution, Hamidah
Jambura Journal of Biomathematics (JJBM) Volume 3, Issue 2: December 2022
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34312/jjbm.v3i2.16878

Abstract

In this study, a mathematical model was studied on the population of the spread of Covid-19 in Medan which the model use an epidemic mathematical model, SEIR (Susceptible, Exposed, Infected, and Recovered). Next, we determine the basic reproduction number R0 using the next generation matrix and the equilibrium point which is analyzed using the Routh Hurwitz criteria. The disease-free equilibrium point is said to be locally asymptotically stable if R01 and the endemic equilibrium point is said to be locally asymptotically stable if R01. Numerical simulation of the model was carried out using real data on the number of Covid-19 cases in Medan and with the help of Maple software. Through the data obtained, the value of R01 indicates that Covid-19 at the time of the study was still contagious to other individuals. Furthermore, based on the simulation formed from the SEIR model with the given initial and parameters, it was found that the greater the contact rate or the transmission rate, the more spread the disease would be and the smaller the cure rate, the more the disease would spread.
ANALISIS MATEMATIKA PADA EFEKTIVITAS VAKSIN MENGENDALIKAN PENYEBARAN COVID-19 DI PROVINSI SUMATERA UTARA Nasution, Hamidah; Alamsyah, Febi; Surbakti, Nurul Maulida
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.229-243.2023

Abstract

Abstrak. Severe Acute Respiratory Syndrome Corona-virus 2 (SARS-CoV-2) ataulebih dikenal Covid-19 adalah virus menular yang sangat berbahaya dan menular dengan cepat. Penyebaran Covid-19 terus menjadi tantangan global yang signifikan dan dapat menimbulkan kematian. Vaksinasi menjadi strategi penting dalam upaya mengendalikan penyebaran penyakit Covid-19 ini. Tujuan penelitian ini adalah menunjukkan efktivitas vaksinasi dalam mengendalikan penyebaran Covid-19 di wilayah Sumatera Utara. Pendekatan yang digunakan adalah melalui pengembangan dan analisis model matematika yang mempertimbangkan faktor-faktor kunci yang mempengaruhi penyebaran penyakit. Dalam model ini, kami menggabungkan parameter vaksinasi dengan variabel-variabel terkait penyebaran penyakit seperti tingkat kontak sosial, kekebalan populasi, dan faktor risiko lainnya. Vaksinasi dilakukan terhadap populasi rentan, Hasil evaluasi menunjukkan bahwa vaksinasi memiliki peran yang signifikan dalam mengendalikan penyebaran Covid-19 di Sumatera Utara. Dengan menggunakan model matematika, dapat memprediksi dampak vaksinasi terhadap penurunan jumlah kasus, tingkat kesembuhan, dan tingkat kematian terkait Covid-19. Selain itu, kami juga menganalisis skenario vaksinasi yang berbeda untuk mengevaluasi efektivitasnya dalam mengurangipenyebaran penyakit Hasil penelitian menunjukkan semakin besar populasi rentanyang divaksin akan memperlambat laju penularan sehingga mengurangi populasi terinfeksi. Analisis dari hasil simulasi menunjukkan bahwa 75% jumlah populasi di Provinsi Sumatera Utara melaksanakan vaksinasi memberikan penurunan jumlah populasi terinfeksi yang signifikan, grafik populasi terinfeksi turun melandai menuju nol, artinya kasus Covid-19 di Provinsi Sumatera Utara dalam kurun waktu tertentu berkurang secara signifikan, Covid-19 bukan pandemi lagi. Hasil penelitian ini dapat menjadi dasar bagi pengambilan keputusan yang berorientasi pada vaksinasi dan upaya pengendalian penyebaran Covid-19 di Sumatera Utara.
Co-Authors Ahmad Rifai Siregar Ahyaningsih, Faiz Ahyaningsih, Faiz Aida Fitri Harun Pakpahan Alamsyah, Febi Ananda, Rizky Anidah, Anidah Asmin Asmin, Asmin Asrin Lubis Ayuniara, Rini BR Sihaholo, Ruth Salisa Cyntia S., Maria DIdi Febrian Dwi Lestari, Riani Elma Batasia Siregar Faigle, Ulrich Farwansyah, Mhd Rio Freddy Giawa Habibi, Rizki Hadi, Rizkiyan Hannum, Syaripah Hashem Beg, Abul Hasibuan, Iman Kamarullah hutabarat, Putri Sari Hutagalung, Goklas Ikhwan, Ali Insan Taufik Ismail Husein, Ismail Izwita Dewi Kana Saputra S Karo, Nur Hidayah Br. Kartika, Dinda Lumban Gaol , Ian Pedrosa Manatap Manihuruk, Hermanto MANSUR AS Manurung, Jeremia Mariani Mariani Mariani Mariani Misgiya, Misgiya Mukhtar Mukhtar Mulyono Mulyono Mulyono, Mulyono Nadya Ramadhani Nainggolan , Desta Asina Nasution , Alvi Sahrin Niska, Debi Yandra Nofertinus Zai, Fidelis Novalia, Essa Nuhrul Huda, Ella Nur Fitriani Nur Halimah Matondang Nur Hidayah Br Karo Nurul Maulida Surbakti Pajariah, Sri Putri Parapak, R Putri Angela Paula Putri Vansia Br. Siahaan Pernanda Tanjung, Alpha Reynaldi Purba, Feronika Paska Putri Sonia Br. Simarmata Rahmadani, Ulfy Rawiyah, Rawiyah Rima Aprilia Riri Syafitri Lubis Roder, Klause Said . Iskandar Sartika, Dewi . Serban, Razvan Sihaloho, Ruth Salisa Silaban, Indah Puspita Simamora, Elmanani Simanjuntak, Dewi Efarina Simanungkalit, Devi Febriany Simarmata, Putri Sonia Siregar, Rudi Sri Dewi Sri Wahyuni Suci Rachmadini, Haliza Syarida Aini, Desti Taruli Marito Silalahi Tri Andri Hutapea Ulfah, Indi Fauziati Ulfy Rahmadani Wahyu Tri Atmojo Widyasari, Rina Zulfahmi Indra, Zulfahmi