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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JURNAL DERIVAT: JURNAL MATEMATIKA DAN PENDIDIKAN MATEMATIKA BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jambura Journal of Biomathematics (JJBM) Milang Journal of Mathematics and Its Applications Journal of Mathematics, Computation and Statistics (JMATHCOS)
Jaharuddin
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Institut Pertanian Bogor
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Earth & Planetary Sciences Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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MODEL PENGENDALIAN INFLUENZA H1N1 DUA STRAIN DENGAN VAKSINASI DAN PENGOBATAN D. NATALIA; T. BAKHTIAR; J. JAHARUDDIN
MILANG Journal of Mathematics and Its Applications Vol. 17 No. 1 (2018): Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (1401.517 KB) | DOI: 10.29244/jmap.17.1.1-16

Abstract

Pada karya ilmiah ini, penyebaran influenza dua strain dimodelkan dengan melibatkan tiga variabel kontrol yaitu vaksinasi dan pengobatan pada masing-masing strain. Akan ditentukan variabel kontrol optimum sehingga dapat meminimumkan populasi terinfeksi berdasarkan empat skenario pengendalian. Prinsip maksimum Pontryagin diterapkan untuk menurunkan sistem persamaan diferensial sebagai kondisi yang harus dipenuhi variabel-variabel kontrol optimum. Kemudian, metode Runge-Kutta orde empat digunakan untuk menentukan solusi numerik dari masalah kontrol optimum. Pada solusi numerik ditunjukkan bahwa pemberian tiga buah kontrol pada model penyebaran influenza H1N1 dua strain memberikan pengaruh yang baik karena dapat menurunkan populasi individu terinfeksi oleh strain satu dan strain dua sampai 99% serta meningkatkan populasi individu yang telah diobati secara efektif sampai 85% pada bulan ke lima.
PENGGUNAAN METODE ANALISIS HOMOTOPI PADA MODEL LOTKA-VOLTERRA DUA SPESIES Jaharuddin; Fahri Novi; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 18 No. 2 (2022): MILANG Journal of Mathematics and Its Applications
Publisher : Dept. of Mathematics, IPB University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (250.706 KB) | DOI: 10.29244/milang.18.2.129-137

Abstract

Dalam artikel ini, metode analisis homotopi digunakan untuk menyelesaikan suatu model Lotka-Volterra dari dua spesies yang bersaing. Dalam hal ini akan ditentukan suatu penyelesaian berupa semi-analitik dari model tersebut. Metodologi penelitian yang dilakukan diawali dengan mendefinisikan suatu operator linear berdasarkan model Lotka-Volterra yang ditinjau, kemudian mengonstruksi suatu persamaan deformasi. Berdasarkan persamaan deformasi ini diperoleh suatu hampiran penyelesaian. Penyelesaian hampiran dari model yang dikaji menunjukkan galat yang relatif kecil. Dalam artikel ini juga diberikan simulasi bahwa jika tingkat intrinsik spesies satu mengalami peningkatan dari 8% hingga 50%, tetapi tingkat intrinsik spesies dua dibuat tetap, maka hasil simulasi menunjukkan bahwa jumlah populasi spesies satu mengalami peningkatan, sedangkan jumlah spesies dua mengalami penurunan.
PENGARUH PERTAHANAN TANAMAN DALAM PENGUSIRAN HAMA PADA MODEL PENANGGULANGAN HAMA TANAMAN TERPADU Ali Kusnanto; Siswandi; Jaharuddin; Farida Hanum
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (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.19.1.43-51

Abstract

Dalam tulisan ini dikembangkan model pengendalian hama tanaman terpadu yang didasarkan pada model mangsa-pemangsa Leslie-Gower. Dalam model ini terdapat unsur pertahanan tanaman (tanaman yang mengeluarkan senyawa/bau) yang akan mampu mengusir sebagian hama yang ada di sekitarnya. Populasi yang terlibat dalam model ini yaitu populasi tanaman, populasi hama, dan populasi pemangsa hama. Tujuan tulisan ini adalah menentukan pengaruh pertahanan tanaman terhadap dinamika populasi yang terlibat. Dari analisis, menghasilkan empat titik tetap. Simulasi dilakukan untuk melihat pengaruh perubahan koefisien efisiensi pertahanan tanaman terhadap kestabilan titik tetap yang diperoleh. Telah ditunjukkan bahwa jika nilai koefisien efisiensi pertahanan tanaman diperbesar, mengakibatkan hama dan pemangsa hama menuju kepunahan dan populasi tanaman akan bertambah banyak.
A FAST COMPUTATION FOR EIGENVALUES OF CIRCULANT MATRICES WITH ARITHMETIC SEQUENCE Sugi Guritman; Jaharuddin; Teduh Wulandari Mas'oed; Siswandi
MILANG Journal of Mathematics and Its Applications Vol. 19 No. 1 (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.19.1.69-80

Abstract

In this article, we derive simple formulations of the eigenvalues, determinants, and also the inverse of circulant matrices whose entries in the first row form an arithmetic sequence. The formulation of the determinant and inverse is based on elementary row and column operations transforming the matrix to an equivalent diagonal matrix so that the formulation is obtained easily. Meanwhile, for the eigenvalues formulation, we simplify the known result of formulation for the general circulant matrices by exploiting the properties of the cyclic group induced by the set of all roots of as the set of points in the unit circle in the complex plane, and also by considering the specific property of arithmetic sequence. Then, we construct an algorithm for the eigenvalues formulation. This algorithm shows a better computation compared to the previously known result for the general case of circulant matrices.
DETERMINAN, INVERS, DAN NILAI EIGEN MATRIKS SKEW-CIRCULANT DENGAN ENTRI BARISAN GEOMETRI Mirza Farhan Azhari; Teduh Wulandari Mas'oed; Sugi Guritman; Jaharuddin; Siswandi
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.19.2.129-140

Abstract

Matriks skew-circulant adalah matriks segi yang entri terakhir setiap baris berpindah ke posisi utama dan berganti tanda disertai pergeseran semua entri lainnya ke posisi berikutnya. Dalam artikel ini, entri dari matriks circulant berupa entri barisan bilangan geometri. Tujuannya adalah merumuskan suatu formulasi sederhana dari determinan, invers, dan nilai eigen dari suatu matriks skew circulant. Formulasi determinan ditentukan dengan menerapkan serangkaian operasi baris dasar dan kolom dasar sampai diperoleh matriks diagonal. Langkah untuk mencari invers dilakukan dengan mengadaptasi metode dalam mencari determinan dan ekuivalensi baris dan kolom pada matriks. Dalam mencari nilai eigen digunakan konsep akar kesatuan (roots of unity) dan subgrup siklik.
Sensitivity Analysis of SI1I2RS Model for Dengue Fever Transmission Blante, Trianty Putri; Jaharuddin, Jaharuddin; Nugrahani, Endar Hasafah
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.23132

Abstract

Dengue fever is a disease caused by dengue virus transmitted through Aedes aegypti mosquitoes. This study discusses the SI1I2RS epidemic model in the spread of dengue fever, assuming that people with this disease can experience severe and mild symptoms. The analysis in this research aims to determine the stability of the equilibrium point, primary reproduction number, parameter sensitivity, and numerical simulation to determine the effect of parameters on the dynamics of the spread of dengue fever. The results of this analysis show two equilibrium points, namely the disease-free equilibrium point, which is locally asymptotically stable when R0 1 and the endemic point, which is locally asymptotically stable when R0 1. Numerical simulations show that the change in the parameter of the average bite of individual mosquitoes in humans has a significant effect on the primary reproductive number where when the moderate acidity of individual mosquitoes in humans is 0.05 and the contact rate of disease transmission from infected mosquitoes to susceptible humans is 0.025, it can suppress the spread of dengue fever. Therefore, individuals must maintain cleanliness and take precautions against the spread of dengue fever.
Model Stokastik Pada Penyebaran Penyakit Tuberkulosis Aziezah, Nur; Sumarno, Hadi; Jaharuddin, Jaharuddin
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 11 No. 2 (2024): Jurnal Derivat (Agustus 2024)
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/jderivat.v10i2.5573

Abstract

Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis. This disease represents a significant global public health challenge. Consequently, a stochastic differential equation model of tuberculosis has been developed. In this context, an analysis examines the impact of complete treatment on the disease-free population distribution, duration of disease-free status, and the probability of remaining disease-free. The analysis shows that as the rate of complete treatment increases, the probability of achieving disease-free status rises, the duration of remaining disease-free shortens, and the number of disease-free individuals grows over time. Keywords: Complete Treatment, Disease-Free Duration, Stochastic Differential Equations, Tuberculosis
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

Abstract

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.
SECURING INFORMATION CONFIDENTIALITY: A MATHEMATICAL APPROACH TO DETECTING CHEATING IN ASMUTH-BLOOM SECRET SHARING Darmawan, Azhar Janjang; Guritman, Sugi; Jaharuddin, Jaharuddin
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 3 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss3pp1989-2002

Abstract

The Secret Sharing Scheme (SSS) based on the Chinese Remainder Theorem (CRT) is a crucial method for safeguarding confidential information. However, this scheme is vulnerable to collaborative cheating involving multiple participants. This study aims to modify the Asmuth-Bloom scheme by introducing two detection mechanisms: Threshold Range Detection and Detection Parameter Verification, to identify and prevent collaborative fraudulent activities. The research design is based on mathematical algorithms and tests the effectiveness of detection against predetermined cheating scenarios using structured parameters. The results indicate that the proposed modifications can accurately detect the manipulation of secret fragments, even in cases involving participant collusion. This robustness is achieved through the mathematical structure of the CRT, which enables the detection of inconsistencies during the secret reconstruction process. In addition to maintaining the efficiency of the original Asmuth-Bloom scheme, these modifications enhance the reliability of the scheme in protecting sensitive data. The study concludes that the implementation of dual detection mechanisms significantly strengthens the security of the SSS, particularly in applications prone to dishonest participant collaboration. Future research is recommended to explore computational efficiency and the implementation of this scheme in real-world environments, such as financial systems and blockchain technology.
Optimal Control Strategies for Syphilis and HIV/AIDS Coinfection Transmission with Cost-Effectiveness Analysis Cahyona, Dwizani Vinoma; Bakhtiar, Toni; Jaharuddin, Jaharuddin
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 2 (2025): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i2.28571

Abstract

Syphilis and HIV/AIDS are global health problems with significant impacts on society. The combination of these two infections can worsen the prognosis of patients and increase the economic strain on the health system. This study aims to develop an optimal control model in managing the spread of syphilis and HIV/AIDS coinfection by considering HIV/AIDS treatment, syphilis treatment, and preventive measures through condom use as dynamic control variables. Pontryagin's maximum principle is used to derive the optimality conditions. To theoretically investigate the impact of the control measures, this study analyzed five strategies related to the implementation of these controls using Scilab-2024.0.0 for simulate and evaluate of their effectiveness. The simulation results show that the combination of three control interventions is more effective in decreasing the prevalence of syphilis and HIV/AIDS coinfection compared to the application of one type of control alone. This combination strategy significantly reduces the infection rate by up to 86.04%, emphasizing the importance of a multifaceted intervention approach rather than a single control measure. Furthermore, a cost-effectiveness analysis was conducted by comparing the costs and effectiveness of various control strategies to determine the most efficient and economically feasible option. The results of the comparison indicate that although integrated intervention is the most effective strategy in minimizing infection rates, a strategy that focuses only on preventive measures through the use of condoms is a more efficient option when considering the balance between budget limitations and control effectiveness.
Co-Authors A. KUSNANTO A. T. WIBOWO Ahkrizal, Afdhal Ali Kusnanto Amalia, Imas Saumi Bib Paruhum Silalahi Blante, Trianty Putri Cahyona, Dwizani Vinoma D. NATALIA Darmawan, Azhar Janjang E. N. BANO Ekaputri, Dhea Endar Hasafah Nugrahani Eti Rohaeti Euis Aprianti F. FAHRURRAZI F. HANUM Fahri Novi Farida Hanum Farida Hanum Fikri, Faiqul H. HASANNUDIN H. HERMANSYAH Hadi Sumarno Handoyo, Sapto Mukti I. ALDILLA L. D. OKTAFIANI L. HAKIM Mirza Farhan Azhari N. AIN Nugrahani, Endar H. Nur Aziezah P. SIANTURI Paian Sianturi Rauf, Nurul Maqfirah Sahamony, Nur Fitriyani Siswandi SISWANDI, S. Sugi Guritman T. BAKHTIAR Tan, Elfina TEDUH WULANDARI Toni Bakhtiar