Simulasi Sistem Dinamik Model Matematika Kasus Kecanduan Bermain Gadget Bagi Anak Usia Dini dengan Faktor Pengawasan Orang Tua

Penelitian ini bertujuan untuk membangun model matematika untuk menggambarkan perubahan tingkat kecanduan bermain gadget pada anak usia dini tipe SEAR (Susceptible – Exposed - Addicted – Recovered). Model matematika yang telah dibuat kemudian dianalisis kestabilan modelnya. Setelah kestabilan model dianlisis, dilanjutkan dengan simulasi model menggunakan software Maple 18. Simulasi dilakukan sebanyak 3 kali dengan nilai faktor pengawasan orang tua yang berbeda yaitu 0.0084, 0.5217, dan 0.8214. Hasil simulasi menunjukkan semakin tinggi angka pengawasan orang tua maka angka kasus kecanduan bermain gadget bagi anak usia dini lebih cepat menurun.Kata Kunci: Gadget, Model Matematika SEAR, anak usia dini, pengawasan orang tua This research aims to develop a mathematical model to depict the changes in the level of gadget addiction in early childhood of the SEAR type (Susceptible - Exposed - Addicted - Recovered). The mathematical model created is then analyzed for its stability. After the stability analysis, the model is further subjected to simulation using Maple 18 software. The simulation is performed three times with different values of parental supervision factors, namely 0.0084, 0.5217, and 0.8214. The simulation results indicate that the higher the level of parental supervision, the faster the cases of gadget addiction in early childhood decline.Keywords: Gadget, SEAR Mathematical Model, Early Childhood, Parental Supervision

HEALTH PROMOTION ANALYSIS AND SIMULATION ON INCREASING VACCINATION WITH USING THE SRV MODEL IN PINRANG DISTRICT

This study discusses the SRV mathematical model of the rate of people refusing vaccination. The data used is primary data in the form of questionnaire data taken directly from the community in Pinrang district related to the rate of people who refuse vaccination. This research starts from building an SRV model to then perform an analysis and simulation of increased vaccination as a result of the role of the Health Promotion section, determining the balance point, analyzing the stability of the model, determining the value of the basic reproductive number (R0), conducting model simulations using Maple21 software, and interpreting the simulation results. . In this article, a mathematical model of SRV is obtained from the analysis and simulation of increased vaccination as the role of the Health Promotion section; two balance points, namely the free balance point to refuse vaccination and the balance point to refuse vaccination; and the basic reproduction rate R0=0.44721 indicates that the population refuses vaccination is decreasing

Analysis and Simulation of SIRI Model for Dengue Fever Transmission

Objectives: The aim of this study is to obtain SIRI model for dengue fever (DHF) transmission, conduct analysis, and simulation of SIRI model in disease-free and endemic and also to predict the number of DHF cases. Methods/statistical analysis: Dengue fever is caused by a virus carried by the Aedes aegypti and Aedes albopictus mosquitoes, the SIRI model is a modification of the SIR model. Analysis of the SIRI model use the Lyapunov function method, then the data used in the simulation are assuming to show two possible dengue status are disease free and endemic status. The simulation also using the number of dengue case in Makassar city for showing the status of dengue fever transmission in Makassar city. Simulation models using Maple software are to predict the number of dengue cases in the following months. Findings: The results of this study are the SIRI model of the transmission of dengue fever with variables that have recovered can be re-infected with dengue fever, analysis of the SIRI model of dengue transmission provides information that the equation system in the SIRI model which is asymptotically stable, it means that dengue cases always exist at a certain time and certain region. The simulation results of the SIRI model in this study illustrate the number of dengue cases in the following months. While the first simulation found the basic reproduction number is R0 = 0.0366≤1 this means that dengue transmission is at an alarming stage, but the second simulation finds the basic reproduction number R0=31.2733>1, this means that, a person infected with dengue causes eight individuals will be infected with dengue fever, so that it is in the endemic stage, and the last simulation using data of the number of dengue case in Makassar city found = 1, that means, Makassar city is a free disease case for dengue fever transmission. Application/improvements: SIRI model for DHF transmission is a mathematical health application. Model analysis guarantees existence, disease-free or endemic status, while simulation results can be used as a reference in DHF prevention

Optimum Control of SEIR Model on COVID-19 Spread with Delay Time and Vaccination Effect in South Sulawesi Province

The increasing number of cases and the development of new variants of the Covid-19 virus globally including the territory of Indonesia, especially in the province of South Sulawesi are increasingly worrying and need to be prevented. Therefore, this study aims to develop a SEIR model on the spread of Covid-19 with vaccination control, optimal control analysis, stability analysis and numerical simulation of the SEIR model on the spread of Covid-19 in South Sulawesi. This study uses the SEIR epidemic model to predict the spread of Covid-19 in South Sulawesi Province with parameters such as birth rate, cure rate, mortality rate, interaction rate and vaccination. The SEIR model was chosen because it is one of the basic methods in the epidemiological model.  The method used to build the model is a time delay model by considering the vaccination factor as a model parameter, model analysis using the next generation matrix method to determine the basic reproduction number and stability of the Covid-19 distribution model in South Sulawesi. Numerical model simulation using secondary data on the number of Covid-19 cases in South Sulawesi starting in 2021 which was obtained from the South Sulawesi Provincial Health Office. The results obtained are model analysis provides evidence of the existence of optimal control in the model. Based on the results obtained, it can also be seen that vaccination greatly influences the spread of Covid-19 in South Sulawesi, so that awareness is needed for the people of South Sulawesi to follow the government's recommendation to vaccinate to prevent or reduce the rate of transmission of Covid-19 in South Sulawesi

Optimal Control of the SEIR Model of Online Game Addiction Using Guidance and Counseling

The purpose of this research is to develop the SEIR model to deal with online game addiction, identify optimal control strategies through guidance and counseling for students addicted to online games, as well as to analyze and simulate models to predict the proportion of students who manage their online game addiction and those who do not. This research is a theoretical and applied research that determined the equilibrium point, stability, and basic reproduction number (R) of the model. The Pontryagin principle was used to optimize the control of the SEIR model, while Maple was used to simulate the online game addiction model. The results show that the SEIR model can be used to deal with online game addiction. The analysis of the model showed that the basic reproduction number before and after control was R0= 0:2221 and R0= 0; 1342 , respectively, which indicates that the problem of online game addiction can be overcome. The simulation results of the SEIR model showed that optimal control through guidance and counseling can reduce the number of students addicted to online games

Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia

The Aim of this research is construct the SEIR model for COVID-19, Stability Analysis and numerical simu- lation of the SEIR model on the spread of COVID-19. The method used to construct the model is the SEIR model by considering vaccination and isolation factors as model parameters, the analysis of the model uses the generation matrix method to obtain the basic reproduction numbers and the global stability of the COVID-19 distribution model. Numerical simulation models use secondary data on the number of COVID-19 cases in Indonesia. The results obtained are the SEIR model for COVID-19; model analysis yields global stability from the spread of COVID-19; The results of the analysis also provide information if no vaccine, Indonesia is endemic COVID-19. Then the simulation results provide a prediction picture of the number of COVID-19 in Indonesia in the following days, the simulation results also show that the vaccine can accelerate COVID-19 healing and maximum isolation can slow the spread of COVID-19. The results obtained can be used as a reference for early prevention of the spread of COVID-19 in Indonesi

Numerical Solution of SIRS model for Dengue Fever Transmission in Makassar Citywith Runge Kutta Method

The aim of this study was to obtain a SIRS model solution for the spread of dengue fever (DF) using the 4th order Runge-Kutta method. The data used was data on the number of dengue cases in Makassar city. The method used is the 4th order Runge Kutta Method. The results of this study are numerical solutions of the SIRS model on the spread of DF in Makassar city using the Runge Kutta method; Model simulation analysis shown that the estimated number of dengue cases in Makassar city, so that the government can take steps to prevent the spread of dengue in Makassar city

Penyelesaian Persamaan Panas Dimensi Satu dengan Metode Beda Hingga Skema Eksplisit

Penelitian ini merupakan peneltian murni berupa kajian teori yang bertujuan untuk mengetahui penyelesaian persamaan panas dimensi satu dengan menggunakan metode beda hingga skema eksplisit dan mengetahui simulasi persamaan panas dimensi satu. Metode beda hingga skema eksplisit adalah suatu metode alternatif yang digunakan untuk menyelesaiakan persamaan differensial parsial. Langkah pertama pada penelitian ini yaitu membangun dan menganalisis persamaaan panas dimensi satu. Selanjutnya mendiskritisasi persamaan panas dimensi satu dengan menggunakan turunan numerik. Kemudian menyelesaikan persamaan panas dimensi satu dengan menggunakan skema eksplisit. Terakhir, menggunakan program Matlab untuk melakukan simulasi penyelesaian persamaan panas dimensi satu. Hasil simulasi menunjukkan bahwa adanya perubahan suhu dari suhu yang tinggi ke suhu yang lebih rendah yang dipengaruhi oleh waktu karena adanya proses perpindahan panas.Kata Kunci: Persamaan Panas, Metode Beda Hingga, Skema Eksplisit.This research is a pure research in the form of a theoretical study that aims to determine the solution of the one-dimensional heat equation using the finite difference method explicit scheme and to know the simulation of the one-dimensional heat equation. The explicit schema finite difference method is an alternative method used to solve partial differential equations. The first step in this research is to build and analyze the one-dimensional heat equation. Next, discretize the one-dimensional heat equation by using numerical derivatives. Then solve the one-dimensional heat equation using an explicit schema. Finally, using the Matlab program to simulate the solution of the one-dimensional heat equation. The simulation results show that there is a change in temperature from a high temperature to a lower temperature which is influenced by time due to the heat transfer processKeywords: Heat Equation, Finite Difference Method, Explicit Schemati