Development and Extension of Differential Equation Models (SIR, SEIR, and SIS) for COVID-19 Pandemic Analysis

Abstract

The COVID-19 pandemic has demonstrated the critical importance of accurate epidemic modeling for public health decision-making. This study develops and extends classical differential equation models (SIR, SEIR, and SIS) to incorporate real-world factors such as time-varying transmission rates, intervention measures, and population heterogeneity using MATLAB as the computational platform. The research addresses limitations in existing models by introducing dynamic parameters that reflect changing public health policies, vaccination campaigns, and behavioral adaptations during the pandemic. Through comprehensive mathematical formulation and numerical simulation, this work establishes enhanced model frameworks that provide more realistic representations of epidemic dynamics. The extended models demonstrate improved accuracy in capturing the complex behavior of COVID-19 spread while maintaining computational efficiency within the MATLAB environment. Results indicate that incorporating time-dependent intervention factors significantly enhances model predictive capabilities, with validation against real-world data showing improved correlation coefficients ranging from 0.85 to 0.94 compared to classical models. This research contributes to the advancement of epidemic modeling by providing robust, adaptable frameworks that can accommodate the dynamic nature of modern pandemic responses.