Mathematical Modeling of Epidemic Spread Using Nonlinear Differential Equations: Application to the SIR Model and Its Variants

Abstract

This study enhances the understanding of epidemic transmission by employing nonlinear
differential equations within the SIR, SEIR, and SEIRD models, which account for latency and
mortality. These models are useful in estimating what might happen with the disease, how
treatments work, and what policies should be implemented. Our study aims to build and
examine models that describe how an epidemic spreads by dividing the population into health
states (S, I, R, E, D).Utilizing real outbreak data, including from COVID-19, the study calibrates
model parameters and analyzes key epidemic indicators such as peak infection rates and utotal
infections. The baseline SIR model forecasts a peak infection prevalence of 13.2% and a
cumulative infection rate of 89% after 200 days. Simulations with reduced transmission and
increased vaccination show a decrease in total cases to 28%. Validation with epidemic data from
Italy and South Korea indicates high model reliability (R² > 0.96, mean absolute percentage error
< 8%). These results underscore the significance of mathematical modelling in public health
strategies aimed at addressing infectious diseases.