APPLICATION OF SIR MODEL AND EULER'S METHOD IN FORECASTING EPIDEMIOLOGICAL PROCESSES

Abstract

This article investigates the mathematical modeling of infectious disease spread dynamics and the forecasting of their impact on the healthcare system. The analysis of epidemiological processes is based on the classical SIR (Susceptible-Infectious-Recovered) model, where a first-order Euler method, a fundamental numerical approach, is applied to solve the non-linear system of ordinary differential equations. Furthermore, the article evaluates the influence of quarantine measures aimed at reducing contact and transmission rates on the epidemic peak time and the maximum number of active infections. The comparison is visualized through an interactive simulation dashboard developed using web technologies (HTML, CSS, JavaScript, and Chart.js), providing a comparative analysis of scenarios with and without quarantine interventions.