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Unnes Journal of Mathematics
Published by Universitas Negeri Semarang
ISSN : 22526943     EISSN : 24605859     DOI : https://doi.org/10.15294/ujm
Core Subject : Education,
Mathematics
Unnes Journal of Mathematics (UJM) publishes research issues on mathematics and its apllication. The UJM processes manuscripts resulted from a research in mathematics and its application scope, which includes. The scopes include research in: 1. Algebra 2. Analysis 3. Discrete Mathematics and Graph Theory 3. Differential Equation 4. Geometry 5. Mathematics Computation, 6. Statistics.
Arjuna Subject : Matematika - Matematika (Lain-Lain)
Articles 234 Documents
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Implementation of state space method for forecasting the number of patients with HIV/AIDS infectious diseases Wiwik Wiyanti
Unnes Journal of Mathematics Vol 12 No 1 (2023)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v12i1.67789

Abstract

This research concerns about the implementation of the State Space method for forecasting to the number of people with infectious diseases (a case study is the number of people with HIV/AIDS) in the Indonesia. The research was conducted from August 2022 to November 2022. The data obtained from kagle, namely new cases of HIV/AIDS infection. In this research, HIV data from 1990 to 2019 was used for forecast analysis. The forecasting method in this research is State Space method. Predict of new cases will found in 2020, 2021, 2022 and 2023 are 14095,14139, 14167 and 14184 respectively. The forecast analysis result obtained that the mean absolute percentage error is 0,4%.
Stability analysis of MSEITR model on the spread of tuberculosis disease using treatment with DOTS strategy Nila Eva Yusana
Unnes Journal of Mathematics Vol 12 No 1 (2023)
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v12i1.68490

Abstract

Tuberculosis (TB) is an infectious disease that can cause death. Indoneisa is the third country with the highest number of TB patients in the world after India and China. This study discusses the MSEITR mathematical model on the spread of TB disease with the DOTS strategy. The purpose of this research is to form a mathematical model, find the equilibrium point and basic reproduction number, analyze the stability, and simulate the model with maple. The analysis resulted in a DFE and endemic equilibrium point and . From these results it is obtained theorem 1 if then there is only a positive DFE point which is positive and if then there is a DFE and endemic equilibrium point which has a positive value and theorem 2 is obtained which is a DFE point is locally asymptotically stable if and the endemic equilibrium point is locally asymptotically stable if . Furthemore, simulation the model using maple obtained several facts, is the smaller the value of the rate of decline in passive immunity and the probability of individuals infected with TB and the greater the value of the increase in the rate of passive immunity , the rate of latent TB individuals and the rate of active TB individuals undergoing DOTS treatment will accelerate the individual growth rate in each stable subpopulation at the DFE point, menaing that TB disease will disappear faster from the population.
Stability analysis for the equilibrium point of the mathematical model of the spread of HIV/AIDS with treatment in the classification of sufferers’ symptoms Sherly Marlinda; Stevanus Budi Waluya
Unnes Journal of Mathematics Vol 12 No 2 (2023): Unnes Journal of Mathematics
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v12i2.71276

Abstract

Menurut WHO, pada tahun 2021 sebanyak 650.000 orang meninggal akibat HIV. Ada sekitar 38,4 juta orang yang hidup dengan HIV di dunia, dan sebanyak 1,5 juta orang terinfeksi baru HIV/AIDS. Penelitian ini membahas model matematika SEIAT berupa penyebaran penyakit HIV/AIDS dengan pemberian treatment ARV pada klasifikasi gejala penderita. Tujuan penelitian ini adalah membentuk model matematika, menganalisis kestabilan titik kesetimbangan dan menginterpretasikan simulasi model den gan bantuan program Maple. Berdasarkan hasil analisis diketahui bahwa eksistensi titik kesetimbangan dan kestabilannya bergantung pada nilai reproduksi dasar . Dapat disimpulkan jika , maka hanya terdapat satu titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit. Jika , maka terdapat dua titik kesetimbangan, yaitu titik kesetimbangan bebas penyakit dan titik kesetimbangan penyakit. Analisis kestabilan menunjukkan bahwa titik kesetimbangan bebas penyakit akan stabil asimtotik lokal saat . Sedangkan titik kesetimbangan penyakit akan stabil asimtotik lokal saat . Selanjutnya, simulasi numerik menggunakan program Maple menghasilkan fakta, bahwa dengan diberikannya treatment pada populasi HIV gejala ringan akan menurunkan infeksi penularan virus HIV. Disamping itu, semakin besar treatment yang diberikan pada populasi HIV gejala ringan, gejala kronis, dan positif AIDS akan memberikan pengaruh dalam menurunkan infeksi gejala penyakit.
The influence of Allee effect, refugia, and alternative food on a three-species predator-prey model Haya Rohmatunnisa; Tri Sri Noor Asih; Stevanus Budi Waluya; Muhammad Fajar Safaatullah
Unnes Journal of Mathematics Vol 12 No 2 (2023): Unnes Journal of Mathematics
Publisher : Universitas Negeri Semarang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15294/ujm.v12i2.76820

Abstract

This research presents a mathematical model for a three-species predator-prey system, incorporating the Allee effect, refugia, and alternative food. The interactions between prey and intermediate predator, as well as intermediate predator and top predator, are modeled using Holling type II response functions. The resulting system of nonlinear equations yields four equilibrium points, one unstable and three stable locally. Analytical calculations indicate that refugia and alternative food minimally affect the top predator's population growth, while the Allee effect influences the growth of prey and intermediate predator populations. Numerical simulations further support these findings, highlighting the nuanced impacts of these factors on the dynamics of the three-species system.

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