The aims of this study are: to build a SIPA model on the spread of HIV/AIDS; analyse and simulation of SIPA model and to predict the spread of HIV/AIDS. An applied mathematics for Analysis of the SIPA model in case of HIV/AIDS spreading using the Jacobi matrix method to obtain eigenvalues in two conditions, namely endemic and disease-free, while the simulation model uses Maple with initial value data in the form of assumptions represented in research. The research result are the mathematical SIPA model of HIV/AIDS spreading which is a system of differential equations. The analysis of the model gives the value of the disease-free equilibrium point and the asymptotically stable endemic equilibrium point. The results also found that the basic reproduction number was R0=0.0067 for disease-free conditions and R0=2.7944 for endemic conditions indicating the condition of HIV/AIDS spreading cases in the population. The simulation results found that there is a very significant difference between the numbers of AIDS populations when free from disease and during endemic conditions, so that attention is needed for the government to be able to tackle the spread of HIV/AIDS.
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.
This study discusses the numerical solution of the Susceptible-Infected-Recovered (SIIR) transmission model for Tuberculosis (TB) transmission in South Sulawesi. The data used is secondary data from the number of Tuberculosis (TB) sufferers in South Sulawesi from the South Sulawesi Provincial Health Office. The discussion begins with a study of the SIIR model, then builds a time delay SIIR model on the spread of tuberculosis. Next, simulate the delay time SIIR model to find out the number of tuberculosis cases in South Sulawesi. Determining the parameters, simulation and analysis of the results in this study obtained a graph of the movement of the SIIR model of time delay of the spread of tuberculosis with real data. After analyzing the numerical simulation, it is seen that there is a tendency for the spread of Tuberculosis (TB) in South Sulawesi. The SIIR model is a four-dimensional non-linear differential equation. The results of the modeling are simulated using MatLab software to predict the number of TB cases so that early prevention measures are the government’s attention to prevent the spread of Tuberculosis (TB) in South Sulawesi.
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