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

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.