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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi NUMERICAL (Jurnal Matematika dan Pendidikan Matematika) Jurnal Abdimas PHB : Jurnal Pengabdian Masyarakat Progresif Humanis Brainstorming Griya Journal of Mathematics Education and Application MATHunesa: Jurnal Ilmiah Matematika Bulletin of Applied Mathematics and Mathematics Education
Budi Priyo Prawoto
Universitas Negeri Surabaya
Automotive Engineering Computer Science & IT Education Mathematics Mechanical Engineering Public Health

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Peningkatan Kemampuan Guru dalam Menggunakan Wolfram Cloud dalam Pembelajaran Matematika Dwi Nur Yunianti; Raden Sulaiman; Yuliani Puji Astuti; Budi Priyo Prawoto; Rudianto Artiono
Jurnal Abdimas PHB : Jurnal Pengabdian Masyarakat Progresif Humanis Brainstorming Vol 5, No 2 (2022): Jurnal Abdimas PHB : Jurnal Pengabdian Masyarakat Progresif Humanis Brainstormin
Publisher : Politeknik Harapan Bersama

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30591/japhb.v5i2.3103

Abstract

Penggunaan wolfram cloud diperlukan untuk mendukung keefektifan pembelajaran matematika selama masa pandemi Covid-19. Software ini dapat digunakan tidak hanya untuk menggambar grafik, visualisasi suara, menganalisa model bidang 3D tetapi juga dalam menyelesaikan permasalahan terkait kalkulus seperti persamaan kuadrat, turunan dan integral. Berdasarkan wawancara dengan beberapa guru matematika di MTsN 3 Jombang, 70% guru belum pernah menggunakan aplikasi wolfram cloud. Oleh karena itu mengingat pentingnya kompetensi guru dalam menguasai teknologi pada suatu pembelajaran maka kegiatan pelatihan wolfram cloud ini perlu diadakan. Berdasarkan hasil pre test dan posttest, terjadi peningkatan pemahaman tentang konsep persamaan kuadrat dan wolfram cloud yaitu dari rata-rata 41,4 menjadi 76,1. Selain itu, seluruh peserta pelatihan menyatakan kegiatan dapat menambah pemahaman terkait wolfram cloud dengan skor 4.46 (skala 5) dan dapat digunakan untuk pembelajaran matematika berbasis TPACK (Technological Pedagogical Content Knowledge) di sekolah dengan skor 4.23 (skala 5).
Stability Analysis of Monkeypox Transmission Model by Administering Vaccine Lailatuz Arromadhani; Budi Priyo Prawoto
Numerical: Jurnal Matematika dan Pendidikan Matematika Vol. 7 No. 1 (2023)
Publisher : Institut Agama Islam Ma'arif NU (IAIMNU) Metro Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25217/numerical.v7i1.3481

Abstract

Monkeypox is an infectious disease that affects mammals, including humans and some primates. Monkeypox transmission can be prevented by administering vaccinations to the human population. This study aims to construct and analyze the monkeypox transmission model's stability with vaccination. There are six sub-populations: Vaccinated humans ( ), Susceptible humans ( ), Infected human , Recovered human , Susceptible animal , and Infected human . Several steps are literature study, formulating assumptions, constructing models, finding equilibrium points, searching for reproduction numbers by next-generation matrix, analyzing stability, and numerical simulations using Matlab R02023b. From the model, three equilibria are obtained: disease-free equilibrium points, first endemic equilibrium points, and second endemic equilibrium points. Disease-free equilibrium point will be asymptotically stable at the vaccination rates  and the animal transmission rate of the animal at the rate of . The first endemic equilibrium point ) will be stable for  and . The second endemic equilibrium point  will be stable for  and . Based on numerical simulation results, it is obtained that the higher the vaccination rate and the lower the transmission rate in animals, the faster the transmission of monkeypox infections.
Stability Analysis of Monkeypox Transmission Model by Administering Vaccine Lailatuz Arromadhani; Budi Priyo Prawoto
Numerical: Jurnal Matematika dan Pendidikan Matematika Vol. 7 No. 1 (2023)
Publisher : Institut Agama Islam Ma'arif NU (IAIMNU) Metro Lampung

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25217/numerical.v7i1.3481

Abstract

Monkeypox is an infectious disease that affects mammals, including humans and some primates. Monkeypox transmission can be prevented by administering vaccinations to the human population. This study aims to construct and analyze the monkeypox transmission model's stability with vaccination. There are six sub-populations: Vaccinated humans ( ), Susceptible humans ( ), Infected human , Recovered human , Susceptible animal , and Infected human . Several steps are literature study, formulating assumptions, constructing models, finding equilibrium points, searching for reproduction numbers by next-generation matrix, analyzing stability, and numerical simulations using Matlab R02023b. From the model, three equilibria are obtained: disease-free equilibrium points, first endemic equilibrium points, and second endemic equilibrium points. Disease-free equilibrium point will be asymptotically stable at the vaccination rates  and the animal transmission rate of the animal at the rate of . The first endemic equilibrium point ) will be stable for  and . The second endemic equilibrium point  will be stable for  and . Based on numerical simulation results, it is obtained that the higher the vaccination rate and the lower the transmission rate in animals, the faster the transmission of monkeypox infections.
Stability Analysis of Conventional and E-Cigarette Smokers Behavior Model with Saturation Effects Binti Mu'alafi Suryantini; Budi Priyo Prawoto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of 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.
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.
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.
A mathematical model of malaria transmission dynamics with multi-stage infection and dual treatment pathways Panca Dewi Fitriyana; Budi Priyo Prawoto
Bulletin of Applied Mathematics and Mathematics Education Vol. 6 No. 1 (2026)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12928/bamme.v6i1.16070

Abstract

Malaria remained a complex global public health challenge due to the interplay between biological transmission and human treatment-seeking behavior. This study developed a deterministic mathematical model incorporating two levels of infection severity (mild and severe) and dual treatment pathways, namely herbal and medical treatment. The model was formulated as a system of nonlinear ordinary differential equations and analyzed using the Next Generation Matrix method to derive the basic reproduction number , ​, while local stability was examined using the Routh–Hurwitz criterion. The results showed that the disease-free equilibrium was locally asymptotically stable when , indicating the eventual elimination of the disease. Sensitivity analysis revealed that mosquito mortality and transmission rates were the most influential parameters affecting disease spread. Numerical simulations further demonstrated that increasing early-stage treatment, particularly herbal treatment for mild infections, significantly reduced and limited progression to severe cases. These findings highlighted the critical role of early treatment-seeking behavior combined with effective vector control in reducing malaria transmission and supporting long-term elimination strategies.
Co-Authors Berliana Aulia Mahdi Binti Mu&#039;alafi Suryantini Dwi Nur Yunianti Kasih Aji Wijayanti Lailatuz Arromadhani Panca Dewi Fitriyana Raden Sulaiman Rudianto Artiono Yuliani Puji Astuti