This study aims to solve the population dynamics model using the Euler method, where the model is a nonlinear differential equation. The research methods used are literature study and simulation methods. In theory, the Euler Method is a numerical method that is often used in solving initial value problems. The Euler method is obtained by decomposing a function into a Taylor series up to two initial terms. This method has an accuracy of one.

This research aims to analyze the increase in HIV/AIDS cases in Medan City with a focus on influencing factors and implications for prevention and education. The research method used is library study, by collecting and analyzing data from literature, documents and related reports from various sources, including scientific journals, books and official reports from health and government organizations. The results of the analysis show that factors such as risky behavior, low levels of public awareness, lack of access to health services, and social stigma have a significant role in increasing HIV/AIDS cases. The implication of these findings is the need to increase efforts in prevention and education, with a focus on increasing awareness, reducing stigma, increasing accessibility of health services, and strengthening collaboration between various stakeholders in addressing this problem. This research makes an important contribution to understanding the dynamics of HIV/AIDS epidemiology in Medan City and provides a basis for developing more effective intervention strategies.