Mathematical Modeling of Epidemic Spread Using SIR Models

Abstract

Mathematical modeling has become an important tool for understanding the spread of infectious diseases within populations. Among various models used in epidemiology, the SIR model is one of the most widely applied frameworks for studying epidemic dynamics. The SIR model divides a population into three main compartments: Susceptible (S), Infected (I), and Recovered (R). Individuals move from the susceptible group to the infected group through contact with infected individuals, and eventually transition to the recovered group after gaining immunity or recovering from the disease. the use of differential equations in the SIR model to analyze how infectious diseases spread over time. the interaction between different population groups and predicts how the number of infected individuals changes during an epidemic. Key parameters such as the infection rate and recovery rate play an important role in determining the speed and intensity of disease transmission. By analyzing these parameters, the SIR model can estimate important epidemiological indicators such as the basic reproduction number, which measures how many new infections are generated by one infected individual in a susceptible population.