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All Journal Beta: Jurnal Tadris Matematika Jurnal Natural
Tri Widjajanti Tri Widjajanti
Program Studi Matematika, Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Papua
Agriculture, Biological Sciences & Forestry Chemistry Education Mathematics Physics Social Sciences

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Model KAC WALKS untuk Persamaan Difusi Dimensi Dua Irma Elisabeth Toto; Tri Widjajanti; Andi Fajeriani Wyrasti
Beta: Jurnal Tadris Matematika Vol. 6 No. 1 (2013): Beta Mei
Publisher : Universitas Islam Negeri (UIN) Mataram

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Abstract

Penelitian ini bertujuan menurunkan Model Kac Walks dengan menggunakan Gerak Brown untuk memperoleh persamaan difusi dimensi dua.Difusi merupakan peristiwa mengalirnya atau berpindahnya suatu zat dalam pelarut dari bagian berkonsentrasi tinggi ke bagian yang berkonsentrasi rendah.Difusi dapat dimodelkan atau dinyatakan dalam bahasa matematika, yaitu persamaan difusi yang merupakan persamaan diferensial parsial.Ada beberapa metode yang diketahui untuk membentuk persamaan difusi, diantaranya adalah metode berdasarkan Hukum Fick dan berdasarkan Model Kac Walks.Dalam penelitian ini, metode yang digunakan adalah Model Kac Walks yang pada dasarnya menggunakan Gerak Brown, yaitu pergerakan partikel-partikel yang bergerak terus menerus dalam suatu pola tak beraturan dengan kecepatan tertentu. Hasil dari penelitian ini adalah mendapatkan persamaan difusi dimensi dua dengan cara mengasumsikan pergerakan partikel, identifikasi pergerakan partikel secara probabilistik dan membentuk persamaan difusi dimensi dua dengan menggunakan distribusi peluang dan perluasan Teorema Deret Taylor.
SYARAT PERLU SUATU OPERATOR LINEAR A SEBAGAI GENERATOR DARI FUNGSI KOSINUS COS Tri Widjajanti Widjajanti
Jurnal Natural Vol. 6 No. 2 (2007): Jurnal Natural
Publisher : FMIPA Universitas Papua

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This paper will discussed a linear operator A as generator of cosine function Cos by determining the necessary conditions for operator A as a generator of cosine function Cos.
MODEL SIR (SUSCEPTIBLE, INFECTED, REMOVED) PENYEBARAN COVID-19 DI PROVINSI PAPUA BARAT: MODEL SIR (SUSCEPTIBLE, INFECTED, REMOVED) PENYEBARAN COVID-19 DI PROVINSI PAPUA BARAT Triono Wahyu Diamtoro; Tri Widjajanti Widjajanti; Dariani Matualage
Jurnal Natural Vol. 17 No. 2 (2021): JURNAL NATURAL
Publisher : FMIPA Universitas Papua

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30862/jn.v17i2.146

Abstract

Coronavirus Disease 2019 (COVID-19) is an infectious disease that has been declared a global pandemic by the World Health Organization (WHO). Indonesia is one of the countries affected by this disease and has spread to all provinces including West Papua Province. The purpose of writing this article is to determine a model for the spread of COVID-19 in West Papua, to analyze the point of equilibrium and stability and to determine the basic reproduction number R_0 model. The model used is the SIR epidemiological model and to analyze the equilibrium point and data collection, the author used the Mapple 13 application. The result of this study are a mathematical model based on the assumptions of the spread of COVID-19 in West Papua namely:dS/dt=-βSI/N.dI/dt=βSI/N-αI.dR/dt=αI.The equilibrium obtained based on the equilibrium analysis is the non-endemic equilibrium point, namely E=(S_0,I_0,R_0 )=(N,0,0)which is categorized as stabil neutral. The basic reproduction number (R_0 ) obtained based on the SIR COVID-19 model in West Papua isR_0=β/αwith R_0=1,2. Because the value of R_0>1 means that the spread of COVID-19 in West Papua will increase to become an epidemic. Keywords: SIR, COVID-19, Equilibrium Point, Basic Reproduction Number.
PROYEKSI PERTUMBUHAN PENDUDUK KABUPATEN PEGUNUNGAN ARFAK MENGGUNAKAN MODEL LOGISTIK Kukuh Silvia Dwi Anggraeni; Tri Widjajanti Widjajanti; Rium Hilum Rium Hilum
Jurnal Natural Vol. 18 No. 2 (2022): Jurnal Natural
Publisher : FMIPA Universitas Papua

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30862/jn.v18i2.186

Abstract

Arfak Mountains Regency is an expansion area of Manokwari Regency which was formed based on the law of the Republic of Indonesia Number 24 of 2012 concerning the expansion of Arfak Mountain Regency in West Papua Province. The population growth of the Arfak Mountains Regency which has increased after the expansion can cause social problem in the area. social problems arising from the increase in population can be anticipated by using population growth projection. The purpose of this paper is to determine the logistic model and project population growth in the Arfak Mountains Regency. The results of this study are the mathematical model of population growth in the Arfak Mountains Regency using the logistic model is: The projected population growth of Arfak Mountains Regency in 2030 is people with an intrinsic growth rate of which is .
Penurunan Persamaan Gelombang Air Dangkal (Shallow Water Wave) Menggunakan Hukum Kedua Newton Inayatul Farach Ardianty; Tri Widjajanti Widjajanti; Rium Hilum
Jurnal Natural Vol. 19 No. 1 (2023): Jurnal Natural
Publisher : FMIPA Universitas Papua

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30862/jn.v19i1.206

Abstract

These waves occur when the surface of the water is disturbed by wind, gravity, earthquakes, or landslides on the seabed. Shallow water waves can be modelled or expressed in mathematical language, namely the shallow water wave equation which is a partial differential equation. The shallow water wave equation is a partial differential equation that describes the fluid flow problem. A system is considered shallow water if the depth of the fluid is much less than its wavelength. Shallow water waves are a phenomenon of classical mechanics which can be described by three simple laws called Newton’s laws of motion. The stages in the research include identifying problems, making assumptions, and forming shallow water wave equations using Newton’s Second Law and the law of conservation of mass. The form of the two-dimensional shallow water wave equation is u_t+〖uu〗_x=-gh_x (x,t). and h_t=-[u(D+h)]_x.
ANALISIS DINAMIKA MODEL MANGSA-PEMANGSA DENGAN EFEK ALLEE MULTIPLIKATIF PADA MANGSA DAN PEMBAGIAN POPU-LASI PEMANGSA MENJADI KELAS SEHAT DAN TERINFEKSI La Ode Muhlis; Astifan E Matnai; Rium Hilum; Esther Ria Matulessy; Tri Widjajanti Tri Widjajanti; Zulkarnain Zulkarnain; Sabir Sumarna
Jurnal Natural Vol. 22 No. 1 (2026): Jurnal Natural
Publisher : FMIPA Universitas Papua

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30862/jn.v22i1.311

Abstract

This study examines the interaction between prey and predator populations by incorporating a multiplicative Allee effect on the prey and disease infection in the predator. The mathematical model is constructed using a system of differential equations that integrates logistic prey growth, Holling type II functional response, and compartmental dynamics of healthy and infected predators. The analysis was carried out through nondimensionalization, linearization, and equilibrium point determination using the Jacobian matrix to investigate the local stability of the system. The results indicate that the system possesses several equilibrium points representing population extinction, prey-only existence, and coexistence of prey with either healthy or infected predators. The stability of these equilibria is strongly influenced by parameters such as the prey intrinsic growth rate, the Allee threshold, and the disease transmission rate. Numerical simulations demonstrate that the Allee effect can drive the prey population to extinction when its size falls below a critical threshold, while the disease in predators reduces the growth of healthy predators and thus contributes to the persistence of the prey population. This research enriches the field of mathematical ecology by providing new insights into the role of Allee effects and epidemiology in predator-prey dynamics.
Co-Authors Andi Fajeriani Wyrasti Astifan E Matnai Esther Ria Matulessy Inayatul Farach Ardianty Irma Elisabeth Toto Kukuh Silvia Dwi Anggraeni La Ode Muhlis Matualage, Dariani Rium Hilum Sabir Sumarna Triono Wahyu Diamtoro Zulkarnain Zulkarnain