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Dynamical System of the Mathematical Model for Tuberculosis with Vaccination Ludji, Dian Grace; Sianturi, Paian; Nugrahani, Endar
ComTech: Computer, Mathematics and Engineering Applications Vol 10, No 2 (2019): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v10i2.5686

This research focused on the modification of deterministic mathematical models for tuberculosis with vaccination. It also aimed to see the effect of giving the vaccine. It was done by adding vaccine compartments to people who were given the vaccine in the susceptible compartment. The population was divided into nine different groups. Those were susceptible individuals (S), vaccine (V), new latently infected (E1), diagnosed latently infected (E2), undiagnosed latently infected (E3), undiagnosed actively infected (l), diagnosed actively infected with prompt treatment (Dr), diagnosed actively infected with delay treatment (Dp), and treated (T). Basic reproduction number was constructed using next-generation matrix. Sensitivity analysis was also conducted. The results show that the model comprises two equilibriums: diseasefree equilibrium (T0) and endemic equilibrium (T*). It also shows that there is a relationship between R0 and two equilibriums. Moreover, the disease-free equilibrium point is asymptotically stable local when it is R0 < 1. Then, the disease-endemic equilibrium point is asymptotically stable local when it is R0 > 1. Furthermore, the parameters of ?, ?, and ? are the most important parameter.

ANALISIS SENSITIVITAS PENYEBARAN PENYAKIT TUBERKULOSIS DENGAN REINFEKSI Ludji, Dian Grace
Math Educa Journal Vol 5, No 2 (2021)
Publisher : Universitas Islam Negeri Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/mej.v5i2.2551

This research discusses the mathematical of Tuberculosis disease with reinfection, where there are individuals who are reinfected after undergoing treatment and are declared recover. The mathematical model used is the SEIRE model which is then searched for the equilibrium point, the basic reproduction number ( ), the stability of the equilibrium point and searched the parameter that most influences the increase in the basic reproduction number so that it is emphasized to reduce the transmission of Tuberculosis. The results showed that the SEIRE model is a mathematical model have two equilibrium points (desease free equilibrium and desease endemic equilibrium where both equilibrium poits are locallyn stable in a constant population based on the value of each parameter used. In the SEIRE model, there are four parameters that affect the basic reproduction number, so that must be suppressed to reduce their transmission. The four parameters are transmission rate ( ), infection rate ( ), infection rate ( ), and reinfection rate ( ).

Dynamical System of the Mathematical Model for Tuberculosis with Vaccination Dian Grace Ludji; Paian Sianturi; Endar Nugrahani
ComTech: Computer, Mathematics and Engineering Applications Vol. 10 No. 2 (2019): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v10i2.5686

This research focused on the modification of deterministic mathematical models for tuberculosis with vaccination. It also aimed to see the effect of giving the vaccine. It was done by adding vaccine compartments to people who were given the vaccine in the susceptible compartment. The population was divided into nine different groups. Those were susceptible individuals (S), vaccine (V), new latently infected (E1), diagnosed latently infected (E2), undiagnosed latently infected (E3), undiagnosed actively infected (l), diagnosed actively infected with prompt treatment (Dr), diagnosed actively infected with delay treatment (Dp), and treated (T). Basic reproduction number was constructed using next-generation matrix. Sensitivity analysis was also conducted. The results show that the model comprises two equilibriums: diseasefree equilibrium (T0) and endemic equilibrium (T*). It also shows that there is a relationship between R0 and two equilibriums. Moreover, the disease-free equilibrium point is asymptotically stable local when it is R0 < 1. Then, the disease-endemic equilibrium point is asymptotically stable local when it is R0 > 1. Furthermore, the parameters of β, ρ, and γ are the most important parameter.

Penerapan Metode Runge-Kutta Orde 4 pada Pemodelan Penularan Penyakit Cacar Monyet Dian Grace Ludji; Febrya Christin Handayani Buan
Saintek Lahan Kering Vol 5 No 2 (2022): JSLK DESEMBER 2022
Publisher : Fakultas Pertanian, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/slk.v5i2.1981

Monkeypox is a zoonotic infectious disease caused by the monkeypox virus which belongs to the Orthopoxvirus group. This virus was originally transmitted from animals who innfected with the monkeypox virus to humans, especially rodents and primates. In addition, it can also be transmitted between humans. To make it easier to describe the process of the spread of monkeypox, a mathematical model was created. The mathematical model was made by taking several assumptions based on the nature of charateristics of monkeypox, especially on the pattern of the spread of monkeypox. Based on the assumptions made, this model has two parts to the population, namely the human population is divided into four subpopulations and the animal population is divided in two subpopulations. The model produces a system of non-linear equations that is solved using the Runge-Kutta method of orde 4. The result obtained in this study is a simulation in graphical form. Two simulations were carried out using different parameter values. The parameter is the rate of human infection from animals. The simulation results show that when the value of the human infection rate from animals is reduced, the disease will disappear within a certain time. So that, one of the factor that can be suppressed so that the spread of monkeypox is controlled is the rate of human infection from animals.

Pemetaan Hasil Prediksi Nilai Produk Domestik Regional Bruto (PDRB) Provinsi Nusa Tenggara Timur Dengan Pendekatan Spasial Panel Dinamis Febrya Christin Handayani Buan; Dian Grace Ludji
Saintek Lahan Kering Vol 6 No 1 (2023): JSLK JUNI 2023
Publisher : Fakultas Pertanian, Universitas Timor

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32938/slk.v6i1.2247

The Province of East Nusa Tenggara (NTT) is categorized as a lagging region based on the value of Gross Regional Domestic Product (GRDP) and belongs to the lowest group at the national level. This underdevelopment has become a special concern for the government in every work program. This condition is an appropriate reference for periodic analysis in a certain time series. The analysis is carried out in various aspects that are dynamic by paying attention to spatial conditions, because each region has different characteristics. One of the main concerns is the value of GRDP, which is a measure of the welfare of a region. The estimation of the regency / city GRDP value model in NTT Province has been carried out, so the existing model is then used for prediction analysis based on updated real time data which is then mapped to see the distribution of GRDP values as a description of actual conditions. The prediction process is carried out using a method that is able to accommodate the characteristics of spatial data and a combination of time series and cross section data, so the appropriate method is dynamic panel spatial. The prediction results obtained the accuracy value of the Mean Absolute Percentage Error (MAPE) criterion of 7.47%, which means less than 20%, so it can be concluded that the dynamic panel spatial models is the right method to be used to forecasting the value of district/city GRDP in NTT Province for the next period of time. The prediction results obtained by the distribution of GRDP values are divided into four categories, namely low, medium, high and very high, which are marked by different colors on the mapping.

Pembuktian Struktur Peubah Instrumen Blundell-Bond Generalized Method of Moment (BB-GMM) Estimator Model Regresi Panel Dinamis Febrya Buan; Dian Grace Ludji; Osniman Paulina Maure
Leibniz: Jurnal Matematika Vol. 3 No. 1 (2023): Leibniz: Jurnal Matematika
Publisher : Program Studi Matematika - Fakultas Matematika dan Ilmu Pengetahuan Alam Universitas San Pedro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.59632/leibniz.v3i1.221

Pemodelan regresi panel dinamis dapat mengakomodir gabungan data cross section, time series dan lag time. Adanya lag time peubah respon dalam model mengakibatkan permasalahan endogenitas, yaitu suatu kondisi korelasi antara lag peubah respon dengan error mengakibatkan tidak terpenuhinya sifat kebaikan penduga. Penyelesaian permasalahan tersebut dengan membentuk peubah instrumen yang merupakan proyeksi linier lag peubah respon dari model first diference dan model level regresi panel dinamis yang diestimasi dengan prosedur BB-GMM estimator. Penelitian ini bertujuan untuk membuktikan validitas dari setiap peubah instrumen yang terbentuk dari model regresi panel dinamis. Hasil penelitian empiris diperoleh himpunan peubah instrumen model first diference yang valid yaitu dan himpunan peubah instrumen model level adalah (yi1, yi2,...,yT-2) dan himpunan peubah instrumen model level adalah (yi2, yi3,...,yt-1)

Comparison of Optimal Control Effect from Fungicides and Pseudomonas Fluorescens on Downy Mildew in Corn Ludji, Dian Grace; Hurit, Roberta Uron; Manek, Siprianus Septian; Ndii, Meksianis Z
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.v5i1.23153

Downy mildew is a disease that continues to infect corn crops in Timor Tengah Utara regency, reducing the amount of crop production and making corn farmers suffer losses. Farmers continue to look for ways to control downy mildew. Two treatments are commonly used by farmers, namely spraying Fungicides and Pseudomonas Fluorescens simultaneously in one unit of time, but have not resulted in optimal production. Therefore, this research is important to get a more optimal way to control find downy mildew. In this paper, we determine the optimal model of downy mildew control in corn plants by comparing the use of Fungicides and Pseudomonas Fluorescens. This research begins by forming a dynamic mathematical model consisting of six populations, namely four corn populations (Sh, F , P , Ih) and two populations of infecting fungi (Sv , Iv ). Then they obtained the basic reproduction number (R0) and two equilibrium points, namely the disease-free equilibrium and the disease-endemic equilibrium which has asymptotic stability. Numerical simulation results based on optimal control analysis with the minimum Pontryagin principle show that using fungicides can reduce the number of plants infected with downy mildew. Therefore, control by using fungicides is necessary and recommended increasing the number of downy mildew infected plants.

Pengaruh Vaksinasi Pada Anjing Terhadap Tingkat Penularan Rabies Menggunakan Pemodelan Dinamik Ludji, Dian Grace; Bobu, Fetronela Rambu
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 12 No. 1 (2025): Jurnal Derivat (April 2025) In Press
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/j.derivat.v12i1.7224

Rabies is a disease that attacks the central nervous system (brain) caused by the rabies virus. Rabies is the most frightening infectious disease in the province of East Nusa Tenggara (NTT) where two people in TTU district were reported to have died from the Rabies virus due to being exposed to GHPR. This research was conducted to see the effect of vaccination on dogs on the rate of rabies transmission. The method used is to first create a mathematical model of rabies transmission by adding vaccination variables, then conducting numerical analysis and simulation. The model formed is . This model is formed to see the effect of vaccination in animals on the transmission of rabies in humans. This model has two equilibrium points, namely a disease-free equilibrium point with the results of the analysis of its stability conditions being locally asymptotically stable when and a disease-endemic equilibrium point with its stability conditions being unstable when . This means that rabies will disappear within a certain period of time. Numeric simulation was performed to support the analysis results using MAPLE software. The simulation results show that in more than 120 days rabies will disappear. Vaccination has a significant impact on the transmission of rabies, that is, the greater the rate of vaccination, the faster it will stop the transmission of rabies. Keywords: Dynamic Model, Rabies Transmission, Rabies Vaccine

Pemanfaatan Software Geogebra Untuk Simulasi Tumbukan Antar Partikel Dalam Satu Dimensi Bobu, Fetronela Rambu; Risald; Ludji, Dian Grace; Donuata, Pujianti Bejahida
Kappa Journal Vol 8 No 3 (2024): Desember
Publisher : Universitas Hamzanwadi

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29408/kpj.v8i3.28478

Penelitian yang terkait pemanfaatan media simulasi komputer sangat menarik dalam pembelajaran fisika karena dapat memvisualisasikan konsep – konsep fisika baik dalam bentuk grafik maupun tabel. Salah satu media simulasi yang dapat digunakan adalah geogebra. Tumbukan atau lentingan antar partikel dapat juga disebut sebagai pantulan karena terjadi antar dua benda yang saling berpadu dan memantul akibat dari adanya pantulan tersebut. Peristiwa tumbukan antara dua benda dapat menyebabkan benda saling menjauh, atau saling berpadu dan bergerak dengan kecepatan yang sama. Penelitian ini bertujuan untuk menentukan gambaran simulasi dari benda yang bertumbukan. Metode yang digunakan merupakan desain pemodelan grafik. Hasil dari penelitian menunjukkan bahwa geogebra dapat mempermudah pemahaman konsep-konsep fisika terkait tumbukan seperti hukum kekekalan momentum, energi kinetik, dan koefisien restitusi melalui visualisasi yang interaktif. Selain itu, siswa dapat mengamati perubahan dalam kecepatan, lintasan, dan energi sebelum dan setelah tumbukan.

Pengaruh Vaksinasi Pada Anjing Terhadap Tingkat Penularan Rabies Menggunakan Pemodelan Dinamik Ludji, Dian Grace; Bobu, Fetronela Rambu
Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika Vol. 12 No. 1 (2025): Jurnal Derivat (April 2025)
Publisher : Pendidikan Matematika Universitas PGRI Yogyakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31316/j.derivat.v12i1.7224

Rabies is a disease that attacks the central nervous system (brain) caused by the rabies virus. Rabies is the most frightening infectious disease in the province of East Nusa Tenggara (NTT) where two people in TTU district were reported to have died from the Rabies virus due to being exposed to GHPR. This research was conducted to see the effect of vaccination on dogs on the rate of rabies transmission. The method used is to first create a mathematical model of rabies transmission by adding vaccination variables, then conducting numerical analysis and simulation. The model formed is . This model is formed to see the effect of vaccination in animals on the transmission of rabies in humans. This model has two equilibrium points, namely a disease-free equilibrium point with the results of the analysis of its stability conditions being locally asymptotically stable when and a disease-endemic equilibrium point with its stability conditions being unstable when . This means that rabies will disappear within a certain period of time. Numeric simulation was performed to support the analysis results using MAPLE software. The simulation results show that in more than 120 days rabies will disappear. Vaccination has a significant impact on the transmission of rabies, that is, the greater the rate of vaccination, the faster it will stop the transmission of rabies. Keywords: Dynamic Model, Rabies Transmission, Rabies Vaccine

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