Mathematical Modeling of Epidemics: A Computational Approach

Abstract

The rapid spread of infectious diseases necessitates effective analytical tools for understanding epidemic dynamics and supporting public health decision-making. Mathematical modeling has emerged as a powerful approach for analyzing disease transmission by representing epidemiological processes through differential equations. In this study, a computational framework based on the classical Susceptible–Infected–Recovered (SIR) model is developed to investigate the temporal evolution of an epidemic in a closed population. The proposed model formulates the disease dynamics using a system of nonlinear ordinary differential equations, which are solved numerically through computational simulation using synthetic data. The resulting epidemic curves illustrate key features of disease spread, including the growth phase, peak infection period, and eventual stabilization due to recovery and herd immunity. The impact of epidemiological parameters such as transmission and recovery rates on epidemic severity is analyzed and interpreted graphically. The study demonstrates that computational epidemic modeling provides valuable insights into outbreak progression even in data-limited scenarios. The proposed approach is simple, reproducible, and flexible, offering a foundational framework that can be extended to advanced epidemic models and data-driven predictive techniques.