MATHEMATICAL MODELING OF EPIDEMIC DYNAMICS AND DISEASE SPREAD USING THE SIR MODEL

This article examines the use of mathematical modeling for analyzing and predicting the spread of infectious diseases, focusing on the SIR (Susceptible–Infectious–Recovered) model, which is widely used in epidemiology. A general overview of the model is presented, followed by the derivation of its three fundamental differential equations that describe the dynamics of changes in each population group. Numerical solutions are obtained using Euler’s method for two sample cases, and the results are then analyzed to determine the epidemic peak and the point at which it begins to decline. Additionally, the relationship between the height of the peak and the initial number of susceptible individuals is investigated through graphical analysis. The paper discusses the limitations of both the SIR model and Euler’s method, emphasizing that the choice of parameters—such as infection and recovery rates—significantly affects the modeling results. The purpose of this work is to deepen the understanding of disease transmission mechanisms and to demonstrate how mathematical methods can support the development of effective epidemic control and management strategies. Furthermore, the study highlights the practical importance of mathematical modeling in epidemiology: such models make it possible to predict potential epidemic scenarios, assess the effectiveness of preventive measures (vaccination, isolation, contact restrictions), and optimize the allocation of healthcare resources. The SIR model also serves as a foundation for constructing more complex models—such as SEIR, SIRS, SEIRD, and others—making it a fundamental tool for further research into the dynamics of infectious processes.