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All Journal Jurnal Ilmu Dasar Jambura Journal of Mathematics Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP) Journal of Fundamental Mathematics and Applications (JFMA)
Soemarsono, Annisa Rahmita
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Control & Systems Engineering Decision Sciences, Operations Research & Management Mathematics

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MODEL MATEMATIKA PENYEBARAN VIRUS NIPAH (NiV) DENGAN KONTROL OPTIMAL MENGGUNAKAN METODE PONTRYAGIN MAXIMUM PRINCIPLE (PMP) Ilmayasinta, Nur; Soemarsono, Annisa Rahmita; Aishwaray, Erra Noer Rohmania
Jurnal Ilmiah Matematika dan Pendidikan Matematika Vol 14 No 1 (2022): Jurnal Ilmiah Matematika dan Pendidikan Matematika (JMP)
Publisher : Universitas Jenderal Soedirman

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20884/1.jmp.2022.14.1.5739

Abstract

ABSTRACT. The use of optimal intervention strategies to prevent the spread of Nipah virus (NiV) by applying optimal control approaches is discussed in this article. To begin, we developed a dynamic model of NiV infection as well as three control strategies: public awareness, treatment, and quarantine. The study's goal was to lower the number of affected patients while lowering the three control costs. The Pontryagin maximum concept will be used to characterize optimal control, followed by numerical simulations using the Runge Kutta method of order 4. The simulation findings suggest that the optimal control technique is effective in reducing the appropriate cost of infected individuals while also providing three ideal controls. Early control measures can also effectively prevent the spread of the Nipah virus, according to numerical simulations.Keywords: Mathematical Modelling, Nipah Virus (NiV), Optimal Control, Pontryagin’s Maximum Principle. ABSTRAK. Artikel ini membahas tentang penggunaan strategi intervensi yang optimal untuk menahan penyebaran virus Nipah (NiV) dengan menggunakan teknik pengendalian yang optimal. Pertama, kami membuat model dinamis infeksi NiV dan tiga strategi kontrol yaitu kontrol kesadaran masyarakat, pengobatan dan karantina. Tujuan penelitian adalah untuk mengurangi jumlah orang yang teinfeksi dan meminimalkan ketiga biaya pengendalian. Karakterisasi kontrol optimal menggunakan prinsip maksimum pontryagin, yang selanjutnya akan dilakukan simulasi numerik menggunakan metode Runge Kutta orde 4. Hasil simulasi yang dilakukan menunjukkan bahwa teknik kontrol optimal efektif dalam mengurangi jumlah individu yang terinfeksi. Simulasi numerik yang dilakukan juga menunjukkan bahwa strategi pengendalian dini dapat efektif mengendalikan penyebaran virus Nipah.Kata Kunci: Kontrol Optimal, Model Matematika, Prinsip Maksimum Pontryagin, Virus Nipah (NiV).
OPTIMAL CONTROL OF MATHEMATICAL MODELS IN BIOENERGY SYSTEMS AS EMPOWERMENT OF SUSTAINABLE ENERGY SOURCES Nugraheni, Kartika; Soemarsono, Annisa Rahmita; Millah, Nashrul; Anggriani, Indira; Usrotus Wakhidah, Ummi Saydatul
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i1.22482

Abstract

Energy has a very important role in everyday life. Dependence on non-renewable energy increases its vulnerability to supply instability, making it important to seek alternative energy sources to overcome this dependence. Bioenergy is an alternative energy produced from organic materials such as biomass. Control of renewable energy is needed to increase production and empowerment. In this research, a mathematical model of biogas production growth in the form of differential equations formed with optimal control modifications is proposed. Completion of the model is carried out by forming an objective function, as well as determining the Hamilton function and Lagrange function. Numerical simulations in the model show that providing control can increase biogas production as a sustainable energy source.
Application of Optimal Control on Mathematical Model of Drug Distribution with Education and Criminal Law Aspect Padja, Merry Yulianti; Soemarsono, Annisa Rahmita; Fitria, Irma
Jurnal ILMU DASAR Vol 25 No 2 (2024)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/jid.v25i2.42387

Abstract

Drugs are substances that, when used, can impact the body, particularly the central nervous system/brain. Prolonged drug use can lead to various disorders affecting physical, psychological, and social functioning. Generally, drug use cases occur among teenagers due to a lack of education and low literacy levels about the dangers of drug. In this study, control efforts by modeling the problem of drug use will be studied. In this study, modeling the problem of drug users with control efforts will be studied. There were additional controls for preventing drug abuse through school education, contact prevention through security and healthy living campaigns, and the procedures to report all drug abuse activities. The Pontryagin Minimum Principle is used to shows that the optimal controls influence the level of drug user distribution.
A C3 Magic Decomposition on Friendship Graph with Odd Order Nisa, Indah Chairun; Pancahayani, Sigit; Soemarsono, Annisa Rahmita
Jurnal ILMU DASAR Vol 23 No 1 (2022)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/jid.v23i1.23266

Abstract

Let G = (V,E) is graph with a non-empty set V containing vertices and a set of edges E. Also note that if H = {H_i⊆G_i = 1,2,3,...,n} is a collection of subgraphs from G with H_i≅Hj,i ≠ j. If Hi ∩ Hj = ∅ and ⋃n(i-1)Hi = G, then graph G admits a decomposition H. Furthermore, if there are f(v) and g(e) which are vertices and edges labeling at G, the total weight of each subgraph H_i,i = 1,2,3,…,n has the same value, namely ∑_(v∈V(H_i))▒〖f(v)〗+∑_(e∈E(H_i))▒〖g(e)〗= w, then the graph G contains the magic H_i decomposition with w as the magic constant. This research shows that the friendship graph F_n with n = 2k + 1 for k∈N admits a magic -(a,d)-C_3 decomposition with a magic constant w of 29dk + 6a + 15d.
Implementation of Discrete Time Markov Chain Method to Estimate The Transition of Smartphone Brands Usage in Balikpapan Asyrofi, Anang; Anggriani, Indira; Soemarsono, Annisa Rahmita
Jurnal ILMU DASAR Vol 24 No 2 (2023)
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/jid.v24i2.34872

Abstract

The increasingly rapid competition in the industrial world today encourages all companies to be able to compete by prioritizing the products they offer, one of which is smartphones. Indonesia is one of the countries with the largest smartphone market share in Asia, with the number of active smartphone users in Indonesia reaching 177 million people in 2021 according to data released by the Statista research institute in March 2022. With these conditions, many smartphone companies always follow the direction of development of sophisticated communication technology media and offer a variety of complete and attractive facilities to encourage people to buy these products. One method that can be used to model this uncertainty is Discrete Time Markov chain which can be implemented as a tool for decision making and predicting future events. Therefore, this study was conducted to know the shifting pattern of smartphone use by consumers and predict the shift in smartphone market share for the coming period. The results of the study found that the steady state or equilibrium condition was achieved in the 10th period or in 2032 with the steady state percentage of each brand, namely Samsung = 22.49%, Oppo = 20.82 %, Xiaomi = 17.01%, Realme = 11.54%, Vivo = 11.41%, Apple = 10.27%, and other brands = 6.46%. The increase in market share is predicted to occur in the Oppo, Realme, and Vivo brands, while the decrease in market share will occur in the Apple, Samsung, Xiaomi and other brands.
Control Analysis on Dynamic System Model of Tuberculosis Disease with Educational Campaign, Vaccination, and Treatment Ilmayasinta, Nur; Riyantoko, Prismahardi Aji; Soemarsono, Annisa Rahmita; Rochmatin, Ulifatur
Jambura Journal of Mathematics Vol 7, No 1: February 2025
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjom.v7i1.30663

Abstract

Tuberculosis (TB) is caused by bacteria (Mycobacterium tuberculosis) that most commonly attacks the lungs. TB is spread from person to person through the air. When people with pulmonary TB cough, sneeze, or spit, they propel TB germs into the air. By inhaling only a small number of these germs, a person can become infected. Tuberculosis is curable and preventable. Prevention that can be done is by providing education about TB and vaccines. While treatment can be done by treating infected individuals. This study examines the TB epidemic model with the application of control, by finding optimal control solutions using the Pontryagin Minimum Principle method. In this study, three control variables were applied, namely education, vaccination and treatment. Numerical calculations were carried out using the Forward Backward Sweep 4th order Runge Kutta method and and then simulated. The results of the numerical simulation of the TB epidemic model show that by implementing control in the form of education, vaccination, and treatment, the population of infected individuals can be reduced.
Co-Authors Aishwaray, Erra Noer Rohmania Anggriani, Indira Asyrofi, Anang Fitria, Irma Ilmayasinta, Nur Kartika Nugraheni Millah, Nashrul Nisa, Indah Chairun Padja, Merry Yulianti Pancahayani, Sigit Riyantoko, Prismahardi Aji Rochmatin, Ulifatur Usrotus Wakhidah, Ummi Saydatul