Contemporary Mathematics and Applications (ConMathA)

Analysis of the Stability of the Tuberculosis Disease Spread Model

2024-01-09T09:51:10+07:00

This paper discusses the stability analysis of the model for the spread of tuberculosis and the effects of treatment. The authors analyze the dynamic behavior of the model to investigate the local stability properties of the model equilibrium point. The Routh-Hurwitz criterion is used to analyze local stability at the disease-free equilibrium point, while the Transcritical Bifurcation theorem is used to investigate the local stability properties of the endemic equilibrium point. The results of the discussion show that the stability properties of the equilibrium point depend on the value of the basic reproduction number which is calculated based on the Next Generation Matrix (NGM). When the basic reproduction number value is less than one, then the disease-free equilibrium point is locally asymptotically stable, whereas if it is more than one, then the endemic equilibrium point is locally asymptotically stable. Numerical simulations are included to explain the dynamic behavior of disease spread and to understand the effectiveness of tuberculosis treatment in a given population. The simulation results show that treatment in the infected individual phase is known to be more effective than treatment in latent individuals.

Eksplorasi Etnomatika dalam Tatanan Bangun Ruang dan Bangun Datar Pada Kawasan Alun-Alun Kota Surabaya

2023-12-28T19:33:55+07:00

Mathematics is a science that has been studied from elementary to high school and continues to be developed up to university. Mathematical concepts can be linked to social and cultural concepts called ethnomathematics. Ethnomathematics in community life can be implemented in the form of buildings. This research aims to explore geometric shapes and explain mathematical concepts in the Surabaya City Square building as an effort to help understand geometric concepts in flat shapes and spatial shapes. The method used in this research is a qualitative method with an ethnographic approach and literature study. The research results show that Surabaya City Square is a historic building that implements geometric concepts in terms of buildings. Mathematical concepts in the shape of the Surabaya City Square building include the concept of flat shapes consisting of rectangles, triangles, trapezoids, circles and ellipses, as well as the concept of spatial shapes consisting of triangular prisms, blocks, tubes and balls. It is hoped that this research can provide understanding and make learning interesting, especially in mathematics.

Dimensi Partisi pada Graf Hasil Operasi Korona Tingkat-k

2024-02-02T11:09:26+07:00

Graph theory is one of the subjects in Discrete Mathematics that have long been known and are widely applied in various fields. The topics that are often discussed in graph theory include labeling, coloring, chromatic numbers, metric dimensions, and partition dimensions. Partition dimensions are obtained by grouping all the vertices on the graph into a number of partition classes, then determine the distance of all vertices to each partition class to get a representation. Partition class which representations have different coordinate vectors is called resolving partition. The minimum cardinality of resolving partition is called partition dimensions of the graph. The purpose of this study is to determine the partition dimensions of level corona operation graphs which are GÊ˜^kP_m, GÊ˜^kC_mand GÊ˜^kK_m, where G, P_m, C_m and K_m are connected non trivial graph, path graph, circle graph and complete graph respectively, and any integer kâ‰¥1.

Model Petri Net Pengajuan KKN Mahasiswa Universitas Lampung

2024-01-29T11:15:59+07:00

The Petri Net (PN) model is a powerful mathematical representation for describing dynamic systems involving processes, states, and interactions between its elements. The use of the Petri Net Model has been applied in various contexts, in this research the Petri Net is used to represent the KKN (Real Work Lecture) application flow for students at the University of Lampung. This modeling provides a clear visual representation of the steps required, the stages that must be passed, and the relationships between elements in the KKN application process. This Petri Net Model analysis helps in identifying potential points that can cause delays or errors in the KKN application process. With a better understanding of inter-entity interactions and process flows, improvements and optimization of KKN application procedures can be implemented. The research results show that the use of the Petri Net Model in the context of KKN applications for Lampung University students has great potential to increase efficiency, reduce errors, and speed up the application process.

Prediksi Inflasi, Tingkat Suku Bunga, dan Nilai Ekspor dengan Vector Autoregressive dan Estimator Deret Fourier Simultan

2024-01-17T13:29:00+07:00

In the face of global economic uncertainty, predictions of the value of inflation, interest rates, and the value of exports are becoming increasingly crucial. This is also closely related to the SDGs in goals 8 and 9, namely on Decent Work and Economic Growth as well as Industry, Innovation, and Infrastructure. This study discusses the use of Vector Autoregressive (VAR) methods and Fourier series estimators to improve the accuracy of predictions of these economic variables. The data used are the inflation, export value, and BI Rate sourced from Bank Indonesia and Badan Pusat Statistik with a monthly period and starting from the beginning of 2010 to September 2023. After analysis, the best method was obtained, namely the Fourier series estimator which included cosine and sine components with oscillation parameters 6 with MAPE 1.51% on the inflation value, 1.65% on the interest rate, and 3.03% on the export value. By considering the interaction between economic variables, the prediction results are expected to provide deeper understanding, support decision-making at the macroeconomic level, and assist governments, central banks, and market participants in identifying risks and planning export strategies.