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All Journal Jurnal Matematika Journal of Mathematical and Fundamental Sciences Jurnal Penelitian Pendidikan IPA (JPPIPA) JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Mathematics ComTech: Computer, Mathematics and Engineering Applications MES: Journal of Mathematics Education and Science Indonesian Journal of Electrical Engineering and Computer Science Jambura Journal of Biomathematics (JJBM) Milang Journal of Mathematics and Its Applications Aceh International Journal of Science and Technology Journal of Mathematics, Computation and Statistics (JMATHCOS) MILANG Journal of Mathematics and Its Applications

Paian Sianturi

Department Of Mathematics, Bogor Agricultural University, Jl. Meranti, Kampus IPB Dramaga, Bogor 16680, Indonesia

Author-ID : 3284883

Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemical Engineering, Chemistry & Bioengineering Chemistry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Materials Science & Nanotechnology Mathematics Mechanical Engineering Physics Transportation

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Modeling and Control of the Extreme Ideology Transmission Dynamics in a Society Nur Azizah; Toni Bakhtiar; Paian Sianturi
Jambura Journal of Mathematics Vol 5, No 1: February 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

In this work, we propose a mathematical model to analyze the spread of extreme ideology in society. The so-called SERTA model divides the entire population into five compartments, namely susceptible, extremist, recruiter, treatment, and aware, to describe the state of the willingness of community members toward extreme ideology. We first present a model with constant control, i.e., a model without a dynamical control instrument, and provide the stability analysis of its equilibrium points based on the basic reproduction number. We then reformulate the model into an optimal control framework by introducing three control variables, namely prevention, disengagement, and deradicalization, to enable intervention of the dynamical process. The optimality conditions are obtained by employing Pontryagin's maximum principle, showing the optimal interdependence of state, co-state, and control variables. Numerical simulations based on the well-known Runge-Kutta algorithm and forward-backward sweep method are carried out to evaluate the effectiveness of control strategies under different scenarios. From the simulation results, it is found that by applying the three controls, the optimum solution is obtained. Besides that, in this study, disengagement contributes the most effect in suppressing extremist and recruiter populations, both by using single control and multiple controls.

The Analysis of SEIRS-SEI Epidemic Models on Malaria with Regard to Human Recovery Rate Resmawan Resmawan; Paian Sianturi; Endar Hasafah Nugrahani
Aceh International Journal of Science and Technology Vol 6, No 3 (2017): December 2017
Publisher : Graduate Program of Syiah Kuala University

This article discusses SEIRS-SEI epidemic models on malaria with regard to human recovery rate. SEIRS-SEI in this model is an abbreviation of the population class used in the model, ie Susceptible, Exposed, Infected, and Recovered populations in humans and Susceptible, Exposed, and Infected populations in mosquito. These epidemic models belong to mathematical models which clarify a phenomenon of epidemic transmission of malaria by observing the human recovery rate after being infected and susceptible. Human population falls into four classes, namely susceptible humans, exposed humans, infected humans, and recovered humans. Meanwhile, mosquito population serving as vectors of the disease is divided into three classes, including susceptible mosquitoes, exposed mosquitoes, and infected mosquitoes. Such models are termed SEIRS-SEI epidemic models. Analytical discussion covers model formation, existence and stability of equilibrium points, as well as numerical simulation to find out the influence of human recovery rate on population dynamics of both species. The results show that the fixed point without disease ( ) is stable in condition and unstable in condition . The simulation results show that the given treatment has an influence on the dynamics of the human population and mosquitoes. If the human recovery rate from the infected state becomes susceptible to increased, then the number of infected populations of both species will decrease. As a result, the disease will not spread and within a certain time will disappear from the population.

PENGARUH LAJU VAKSINASI PENYEBARAN PENYAKIT COVID-19 DENGAN VAKSINASI DUA DOSIS Arindria Sekar Putri Valentinna; Ali Kusnanto; Paian Sianturi; Hadi Sumarno; Ngakan Komang Kutha Ardana
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 2 (2023): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.19.2.117-128

Penyakit Coronavirus 2019 (Covid-19) adalah penyakit karena virus SARS-CoV-2. Upaya melawan penyebaran penyakit ini salah satunya dengan vaksinasi. Penyebaran Covid-19 dan proses vaksinasi dua dosis ini dimodelkan menggunakan model matematika SEIV1V2RS. Penelitian ini bertujuan untuk melihat pengaruh laju vaksinasi terhadap perubahan bilangan reproduksi dasar (. Berdasarkan analisis terhadap sensitivitas parameter, yang memiliki pengaruh signifikan terhadap adalah laju efektif penularan penyakit, laju vaksinasi dosis 1 dan laju vaksinasi dosis 2. Dari data yang dipilih pada penelitian ini menunjukkan bahwa jika hanya vaksinasi dosis 1 yang dilakukan maka lajunya harus dinaikkan sebesar 50% baru dapat membuat penyakit akan hilang. Tanpa vaksinasi dosis 1, laju vaksinasi dosis 2 harus dinaikkan 25 kali lipat agar penyakit akan hilang.

PENERAPAN MODEL PERSAMAAN STRUKTURAL UNTUK EVALUASI KUALITAS KINERJA BIMBINGAN KONSELING SMA NEGERI 1 DRAMAGA Akmal Taufik; Budi Suharjo; Hadi Sumarno; N. K. Kutha Ardana; Abdur Rohman; Ali Kusnanto; Paian Sianturi
MILANG Journal of Mathematics and Its Applications Vol. 20 No. 1 (2024): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.20.1.31-42

Bimbingan konseling (BK) pada jenjang pendidikan SMA memiliki peran penting dalam memberikan layanan konsultasi akademik maupun non akademik kepada para siswa. Oleh karenanya, kemampuan dan kepribadian guru BK, serta fasilitas penunjang yang memadai sangat diperlukan. Penelitian ini bertujuan membangun model empiris untuk mengevaluasi kinerja layanan BK berbasis kepuasan siswa, terhadap faktor-faktor yang memengaruhi kualitas kinerja BK SMA Negeri 1 Dramaga. Penelitian ini melibatkan 125 siswa dengan cara mengisi kuesioner secara online. Pendugaan parameter model dilakukan menggunakan Structural Equation Model (SEM). Tingkat kepuasan siswa secara keseluruhan terhadap layanan BK sebesar 94%. Kemampuan Guru BK dan program kerja konsultasi memiliki peran dominan dalam memengaruhi kepuasan. Layanan informasi BK berpengaruh positif terhadap kepuasan, sedangkan faktor kepribadian, fasilitas ruang diskusi, dan program kerja klasikal berpengaruh negatif terhadap kepuasan siswa. Upaya untuk meningkatkan kualitas kinerja BK SMA Negeri 1 Dramaga diprioritaskan melalui peningkatan kinerja program kerja klasikal dengan memperbaiki kualitas penyampaian informasi seputar perguruan tinggi.

The Analisis Sensitivitas Model SEIRV Pada Penyebaran Penyakit Covid-19 Di Indonesia: Sensitivity Analysis of the SEIRV Model on the Spread of Covid-19 Disease in Indonesia Nabila, Nabila; Sianturi, Paian; Bukhari, Fahren
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 8 No 1 (2023): March - August 2023
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v8i1.3438

Model SEIRV dibentuk dengan melihat pada perlakuan terhadap orang yang terinfeksi di Indonesia dengan pembagian subpopulasi terinfeksi menjadi tiga: subpopulasi terinfeksi dirawat di rumah sakit, terinfeksi tidak teridentifikasi, dan terinfeksi isolasi mandiri. Model ini dianalisis sifat kestabilan titik tetapnya dan menganalisis parameter mana yang paling peka terhadap perubahan simulasi model. Model ini memiliki titik tetap tanpa penyakit yang stabil asimtotik lokal pada kondisi bilangan reproduksi dasar kurang dari satu dan titik tetap endemik stabil asimtotik lokal pada kondisi bilangan reproduksi dasar lebih dari satu. Hasil analisis sensitivitas menunjukkan ada tiga parameter yang memiliki pengaruh besar terhadap model: laju transmisi penyakit dari subpopulasi rentan menjadi terekspos, laju kesembuhan subpopulasi terinfeksi tidak teridentifikasi, dan laju vaksinasi. Hal yang dapat dilakukan ketika menginginkan kondisi dimana tidak ada lagi wabah Covid-19 adalah menekan laju penyebaran Covid-19, meningkatkan laju kesembuhan subpopulasi terinfeksi tidak teridentifikasi, dan meningkatkan laju pemberian vaksinasi terhadap populasi.

Stability Analysis of a Time-Delayed Disease Transmission Model in Prey–Predator Populations Incorporating a Holling Type II Functional Response Rauf, Nurul Maqfirah; Sianturi, Paian; Jaharuddin, Jaharuddin
Journal of Mathematics, Computations and Statistics Vol. 8 No. 1 (2025): Volume 08 Nomor 01 (April 2025)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/jmathcos.v8i1.7428

Abstrak. This article presents a comprehensive study of a mathematical model describing the spread of infectious disease within a prey–predator population, incorporating the Holling type II functional response and a delay parameter, denoted as τ, representing the incubation or infection period. The model captures the interactions among four population groups: susceptible prey, infected prey, susceptible predators, and infected predators. Through analytical investigation, six fixed points (equilibrium points) of the system were identified. The stability of these fixed points was examined using the eigenvalues of the Jacobian matrix, and one locally stable fixed point was found, while the others were identified as saddle points or unstable. To gain deeper insights into the model’s behavior over time, numerical simulations were conducted for different values of the delay parameter . The results indicate that the presence of a time delay significantly affects the dynamics of all four population groups. Specifically, the infection delay can suppress or slow the spread of the disease by delaying the transition from susceptible to infected classes. Oscillatory behavior emerged in certain population groups when the delay was introduced, especially among infected prey and predators, before gradually stabilizing toward the disease-endemic equilibrium. These findings highlight the critical role of time delay in disease transmission dynamics in ecological systems and provide a framework for further research on delay-induced phenomena in epidemiological models. Keywords: Prey–Predator, Disease Spread, Delay Time, Functional Response, Stability Analysis.

Mathematical Model of COVID-19 Spread with Vaccination in Mataram City Hattamurrahman, Muhammad Putra Sani; Sianturi, Paian; Sumarno, Hadi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 4 (2024): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i4.23113

The COVID-19 pandemic has had a significant impact on public health worldwide.. Mathematical modeling is considered an alternative tool for understanding real-life problems, including the dynamics of COVID-19 spread. This is an applied research that purpose adds vaccination to Zeb et al. (2020) SEIQR model of COVID-19 spread and examines the dynamic of COVID-19 spread in Mataram City. First, we construct the new model by making assumptions. The fixed point and basic reproduction number (R_0 ) are then used to analyze the model using the next-generation matrix method. The next-generation matrix method is utilized to estimate the R_0 in a compartmental disease model. Two fixed points are acquired, specifically the disease-free fixed point, which is locally asymptotically stable under the condition R_0<1 determined by the Routh Hurwitz criterion via linearization using the Jacobi matrix. And the disease-endemic fixed point, which is locally asymptotically stable under the condition R_0>1 indicated by Lyapunov function. The population dynamics when R_0<1 and R_0>1 can also be observed through numerical simulation. The results of a numerical simulation indicate that giving the proportion of number vaccinated 62 per cent is effective in suppressing the number of infections.

ANALISIS MODEL EPIDEMIK SVEIR DENGAN CONTINUOUS TIME MARKOV CHAIN (CTMC) PADA PENYAKIT RUBELLA Eliska, Nur; Sumarno, Hadi; Sianturi, Paian
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 3 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Penyakit rubella yang dikenal dengan sebutan campak Jerman adalah penyakit menular yang disebabkan oleh virus rubella. Penelitian ini mempelajari model dinamika penyebaran penyakit rubella menggunakan model SVEIR yang merupakan modifikasi dari model yang dikembangkan oleh Beraud dan Saito, dengan pendekatan stokastik CTMC. Simulasi dilakukan untuk mengamati pengaruh perubahan: nilai awal, laju infeksi ( ), tingkat efektivitas vaksin ( ), dan laju vaksinasi ( ). Berdasarkan hasil simulasi diperoleh bahwa, perubahan nilai awal mempengaruhi peluang terjadinya wabah. Semakin tinggi laju sembuh dapat menurunkan peluang wabah. Sedangkan semakin tinggi tingkat efektivitas vaksin dan laju vaksinasi menyebabkan nilai semakin rendah serta nilai peluang wabah yang cukup kecil; artinya peluang bebas penyakit semakin besar dan menghilangnya penyakit rubella dari sistem

PENGARUH LAJU PENULARAN PENYAKIT DAN RATA-RATA KONTAK INDIVIDU PADA MODEL KO-INFEKSI HIV/AIDS DAN CACAR MONYET (MONKEYPOX) Luthfiani, Dini Dessya; Sianturi, Paian; Ali Kusnanto; Sumarno, Hadi
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 1 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.18.1.29-39

Cacar monyet (monkeypox) adalah penyakit akibat virus yang ditularkan melalui binatang. Penularan virus cacar monyet ke manusia dari hewan seperti monyet dan hewan pengerat terjadi melalui kontak langsung atau mengonsumsi daging hewan liar yang terkontaminasi. Dalam model ini, populasi hewan dibagi menjadi tiga subpopulasi dan populasi manusia dibagi menjadi sembilan subpopulasi. Hasil analisis diperoleh titik tetap bebas penyakit dan titik tetap endemik. Hasil analisis sensitivitas menunjukkan bahwa pengaruh laju penularan penyakit dan rata-rata kontak individu merupakan parameter yang paling berpengaruh dalam model. Dengan simulasi numerik, ditunjukkan juga bahwa penurunan laju penularan dan kontak individu berimplikasi pada penurunan bilangan reproduksi dasar. Secara berangsur-angsur, tingkat populasi individu terinfeksi akan turun. Dus, pengontrolan kedua faktor tersebut akan mengakibatkan penyebaran penyakit cacar monyet terkendali.

PENGARUH CARA TRANSMISI DAN IMMUNITAS HUMORAL PADA MODEL VIRUS CHIKUNGUNYA Annisa, Mutia; Sianturi, Paian; Ali Kusnanto; Sumarno, Hadi
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : School of Data Science, Mathematics and Informatics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29244/milang.18.2.115-127

Chikungunya merupakan penyakit yang menginfeksi sendi dan otot yang disebarkan oleh nyamuk aedes aegepty dan aedes albopictus. Virus chikungunya dapat menginfeksi sel rentan melalui dua cara, yaitu sel rentan langsung terinfeksi oleh virus ataupun sel rentan terinfeksi oleh sel lain yang sudah terinfeksi. Penelitian ini bertujuan untuk melihat pengaruh cara transmisi dan immunitas humoral pada model matematika virus Chikungunya. Dalam model ini dihasilkan dua titik tetap, yaitu titik tetap bebas penyakit dan titik tetap endemik. Penentuan kestabilan titik tetap dilakukan dengan mencari bilangan reproduksi dasar, sedangkan pemilihan parameter yang berpengaruh dilakukan dengan analisis sensitivitas parameter. Hasil analisis pada model ini diperoleh bahwa agar penyakit menurun dan hilang diperlukan tindakan menurunkan laju transmisi sel rentan oleh sel virus dan sel terinfeksi serta meningkatkan laju produksi antibodi.

Co-Authors Abdur Rohman Abdur Rohman Akmal Taufik Ali Kusnanto Annisa, Mutia Ardana, N K Kutha Ardana, N. K. Kutha Ardana, Ngakan Komang Kutha Arindria Sekar Putri Valentinna Asmaidi Asmaidi Budi Suharjo D. Ananda Osferi Dian Grace Ludji Dini Dessya Luthfiani Eliska, Nur Endar Hasafah Nugrahani Endar Nugrahani Fahren Bukhari Fatimatuzzahroh Hadi Sumarno Hadi Sumarno Hardianti, Wiwik Tri Hattamurrahman, Muhammad Putra Sani Ilmi, Salsabilla Fitri Jaharuddin Julianto, MT Luthfiani, Dini Dessya Mutia Annisa N. K. Kutha Ardana N. K. Kutha Ardana Nabila, Nabila NGAKAN KOMANG KUTHA ARDHANA Niswah Yanfa Nabilah Syams Nugrahani, Endar Nur Azizah Nurul Qorima Putri Praptaningsih, Anggun Putri, Nurul Qorima Rauf, Nurul Maqfirah Resmawan Resmawan Riza Rusdiani Taufik, Akmal Toni Bakhtiar Valentinna, Arindria Sekar Putri Yomi Kharisma Septika

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