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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi Gamatika BAREKENG: Jurnal Ilmu Matematika dan Terapan JURNAL SILOGISME : Kajian Ilmu Matematika dan Pembelajarannya Jurnal Abdimas PHB : Jurnal Pengabdian Masyarakat Progresif Humanis Brainstorming Jurnal Penelitian Pendidikan Matematika dan Sains Griya Journal of Mathematics Education and Application MATHunesa: Jurnal Ilmiah Matematika JANITA
Budi Priyo Prawoto
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Automotive Engineering Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Mathematics Mechanical Engineering Physics Public Health Social Sciences Transportation Other

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PEMODELAN DINAMIKA VIRUS RUBELLA DENGAN RISIKO SINDROM RUBELLA BAWAAN Abadi, Abadi; Artiono, Rudianto; Prawoto, Budi Priyo
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 15 No 1 (2021): BAREKENG: Jurnal Ilmu Matematika dan Terapan
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (473.89 KB) | DOI: 10.30598/barekengvol15iss1pp069-076

Abstract

Rubella is a common cause of childhood rash and fever. It is typically a mild infection but it can be serious condition in pregnant women, as it may cause Congenital Rubella Syndrome (CRS) in the fetus. The study aimed to model and analyze it in order to get picture about the dynamics of the rubella virus transmission. The paper discussed two models of rubella transmission involving child-bearing age women and newly born infants of infected mothers. The models are SEIR-IR without seasonality and SEIR-IR with seasonality. The results from the first model showed that a pitchfork bifurcation occurred in the dynamics of the solution of the system with constant infection rate and the increase of the infection rate value do not make impact to the incidence of rubella among infants. The second model involving seasonality gave interesting dynamics where big seasonality may lead to a more complex dynamics of the solution.
DINAMIKA PENYEBARAN PENYAKIT KOLERA DENGAN ADANYA VAKSINASI Rauf, Tegrid Chintya Ifareyne; Prawoto, Budi Priyo
Jurnal Silogisme : Kajian Ilmu Matematika dan Pembelajarannya Vol 8 No 1 (2023): Juni
Publisher : Universitas Muhammadiyah Ponorogo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24269/silogisme.v8i1.6748

Abstract

Penelitian ini bertujuan untuk menyusun dan menganalisis model penyebaran penyakit Kolera menggunakan model  (Susceptible-Vaccinated-Infected-Recovered-Infected). Model ini memuat empat subpopulasi yaitu rentan ( ), terinfeksi ( ), sembuh ( ), dan tervaksinasi ( ). Tahapan yang dilakukan dalam penelitian ini adalah melakukan studi literatur, menyusun asumsi, menyusun model diagram kompartemen penyebaran penyakit, konstruksi sistem persamaan diferensial sebagai model, mencari titik ekuilibrium, menganalisa kestabilan titik ekuilibrium menggunakan matriks Jacobian, mencari bilangan reproduksi dengan Next-Generation Matrices (NGM), dan simulasi model menggunakan Matlab untuk sinkronisasi hasil analitik dan numerik. Dalam penelitian ini diperoleh dua titik setimbang dari model  penyebaran penyakit kolera, yaitu titik setimbang bebas penyakit  yang akan stabil ketika . Dan sebaliknya jika diambil  nilai  maka titik setimbang bebas penyakit akan tidak stabil dan menjadi titik setimbang endemik .
Transmission Dynamics of Dengue Disease Incorporating Treatment, Mass Awareness, and Wolbachia Intervention Agustina, Rafika Nanda; Prawoto, Budi Priyo
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.39026

Abstract

Dengue Hemorrhagic Fever (DHF) remains a serious global health threat, with transmission dynamics significantly influenced by vector control strategies and human behavior. This study constructs and analyzes a differential equation-based mathematical model to investigate dengue transmission dynamics by integrating three control strategies: medical treatment, mass awareness, and the release of Wolbachia-infected mosquitoes. The basic reproduction number (R0) is derived using the Next Generation Matrix (NGM) method as a threshold quantity for disease transmission. Simulation results demonstrate that when parameter values satisfy the condition R0 1, the system trajectories converge to the disease-free equilibrium, implying that the disease will be eliminated over time. Conversely, modifying parameters δ and p such that R0 1 results in system stability at the endemic equilibrium, indicating disease persistence within the population. This study concludes the importance of controlling these key parameters through integrated interventions to reduce the value of R0 to less than unity
ANALISIS DINAMIK MODEL PENYEBARAN VIRUS NIPAH PADA MANUSIA DAN KELELAWAR DENGAN PENGARUH VAKSINASI Kasih Aji Wijayanti; Budi Priyo Prawoto
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 3 (2025)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v13n3.p378-387

Abstract

Virus Nipah merupakan penyakit zoonosis yang berasal dari kelelawar buah dari genus Pteropus, yang berperan sebagai reservoir alami dan dapat menularkan virus ini kepada manusia tanpa menunjukkan gejala klinis. Tingginya angka kematian serta belum tersedianya terapi yang efektif menjadikan vaksinasi sebagai strategi penting dalam pengendalian penyebaran virus ini. Penelitian ini bertujuan untuk menganalisis dinamika penyebaran virus Nipah antara populasi kelelawar dan manusia dengan mempertimbangkan pengaruh vaksinasi. Model yang digunakan adalah model SVEIR untuk manusia dan model SI untuk kelelawar. Model ini memuat tujuh subpopulasi yaitu manusia rentan (S_H), manusia tervaksinasi (V_H), manusia terpapar (E_H), manusia terinfeksi (I_H), manusia sembuh (R_H), kelelawar rentan (S_B), dan kelelawar terinfeksi (I_B). Didapatkan dua titik kesetimbangan, yakni titik kesetimbangan bebas penyakit T₀ dan titik kesetimbangan endemik T₁. Analisis kestabilan dilakukan terhadap titik kesetimbangan bebas penyakit menggunakan pendekatan Jacobian, serta Next Generation Matrix (NGM) untuk menentukan bilangan reproduksi dasar (R₀). Titik kesetimbangan bebas penyakit stabil ketika memenuhi syarat kestabilan berikut: β₃ < μ_B² / Λ_B. Sedangkan titik kesetimbangan endemik stabil ketika memenuhi syarat berikut:β₃ > μ_B² / Λ_B. Bilangan reproduksi dasar diperoleh dari persamaan berikut: R₀ = (β₃ Λ_B) / μ_B². Jika R₀ < 1 maka penyakit akan punah dari populasi dan jika R₀ > 1 maka penyakit akan tetap endemik dalam populasi. Hasil simulasi numerik menunjukkan bahwa peningkatan laju vaksinasi manusia ω_H dapat menurunkan jumlah individu yang rentan, terpapar, terinfeksi, dan sembuh serta mempercepat pemusnahan infeksi, baik dalam kondisi bebas penyakit maupun endemik. Namun, vaksinasi tidak memengaruhi dinamika populasi kelelawar. Oleh karena itu, strategi pengendalian tambahan pada populasi kelelawar diperlukan guna memutus rantai penularan secara komprehensif. Kata Kunci: Virus Nipah, Vaksinasi, Syarat Kestabilan, Bilangan Reproduksi Dasar, Simulasi Numerik.
Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects Suryantini, Binti Mu'alafi; Prawoto, Budi Priyo
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.40109

Abstract

Smoking behavior is a harmful habit that poses serious health risks and has been regarded as a lifestyle by certain segments of society, regardless of age, gender, or social status. This study develops and analyzes a mathematical model of smoking behavior that classifies between conventional smokers and e-cigarette smokers, incorporates interaction with lung cancer patients, and considers the saturation effect on potential smokers as the number of smokers in the population increases. The method is determining assumptions to create a compartment diagram and construct the model. This model has four equilibrium points. The results show that when R01 1, R02 1, the smoker-free equilibrium point is asymptotically stable. When R01 1, R02 1, the endemic equilibrium point of e-cigarette smokers becomes stable. When R01 1 and R02 1, the endemic equilibrium point of conventional smokers becomes stable. Meanwhile, when R01 1 and R02 1, the endemic equilibrium point of coexistence of conventional and e-cigarette smokers becomes stable. Numerical simulations show that the intensity of smoking transmission affects the dynamics of the system. The lower the transmission rate by conventional and e-cigarette smokers, the faster the transition to a smoker-free population. The saturation effect plays a role in limiting excessive contact between potential smokers and smokers.
Pendekatan Pemodelan Matematika Penyebaran Tuberkulosis Sensitif Obat (TB-SO) dan Tuberkulosis Resisten Obat (TB-RO) dengan Vaksinasi dan Isolasi Berliana Aulia Mahdi; Budi Priyo Prawoto
Griya Journal of Mathematics Education and Application Vol. 6 No. 1 (2026): Maret 2026
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v6i1.1040

Abstract

Tuberculosis (TB) remains a serious public health problem. Based on bacterial susceptibility to anti-tuberculosis drugs, TB is classified into drug-susceptible TB (DS-TB) and drug-resistant TB (DR-TB), where the presence of DR-TB poses a challenge for control because its management is more complex and it has the potential to sustain transmission within a population. Mathematical models can be used to understand the transmission dynamics of DS-TB and DR-TB. This study analyzes the model The novelty of this research lies in the development of a two-strain TB model that simultaneously incorporates strain-specific latent phase separation, differences in transmission rates between strains, and TB-RO-specific isolation interventions within a single framework. The analysis include determining equilibrium points, the reproduction number using next generation matrix, stability analysis, and numerical simulations. Three equilibrium points are obtained: disease-free, TB-RO mono-existence, and coexistence of both strains. Stability analysis at each equilibrium point is carried out using the value of . The analysis is performed through parameter conditions related to the transmission rate of DS-TB and the transmission rate of DR-TB . Sensitivity analysis shows that reducing and has a major impact on suppressing the transmission of DS-TB and DR-TB. In addition, increasing substantially reduces DR-TB transmission by enhancing the isolation of DR-TB cases.
Co-Authors ABADI Agustina, Rafika Nanda Al Faruqy, Abu Hanifah Amalia, Iva Imana Ambarwati, Anggraeny Elvyna Atik Wintarti, Atik Berliana Aulia Mahdi Dwi Juniati I Ketut Budayasa Kasih Aji Wijayanti RADEN SULAIMAN Rauf, Tegrid Chintya Ifareyne RUDIANTO ARTIONO, RUDIANTO Suryantini, Binti Mu'alafi Yunianti, Dwi Nur YUSUF FUAD