Exploring The Future of Health Through The SELR Mathematical Model with Time Delay on The Risk of Diabetes Among Mathematics Students of FMIPA UNM Due to Unhealthy Lifestyles - Muhammad Abdy; Muhammad Isbar Pratama; Syafruddin Side; Minggi, Ilham; Yusuf S.A.P., Andi Muh. Ridho (Universitas Cokroaminoto Palopo, 2025)
This study aims to build a SELR model with a time delay in diabetes cases, analyze the model, and conduct simulations to predict the incidence of diabetes. This study is a combination of theoretical and application studies. The analysis of the SELR model with a time delay is focused on diabetes cases, while the simulation is carried out using Maple Software. The study population was active students of FMIPA UNM, with a sample size of 1,000 students obtained using the Slovin technique. This study produces a mathematical model of SELR with a time delay for diabetes cases represented as a system of differential equations. Model analysis shows the existence of an equilibrium point free from diabetes cases and a stable endemic equilibrium point. In addition, the results of this study found the basic reproduction number (R₀) for cases without a solution of 25.97333855, which means that one individual can affect 25-26 people in the FMIPA UNM environment. However, if the solution is applied, the R₀ value decreases to 0.7502918529, indicating that there is no psychological spread, where each individual does not affect other individuals.