In this paper, we investigate the development of an infectious disease in a population of organisms using a mathematical model described by a system of Ordinary Differential Equations (ODEs) with time-varying parameters. The incorporation of time-dependent parameters enables the model to capture variations in epidemic conditions and disease transmission during different stages of an outbreak, providing a more realistic representation of epidemic dynamics than models with constant coefficients. An analytical solution of the proposed model is obtained using the Method of Functional Corrections (MFC), which provides an efficient framework for analyzing nonlinear epidemic systems without relying on numerical approximations. The analytical expressions derived from the proposed approach provide insight into the influence of model parameters on disease progression and facilitate the qualitative assessment of epidemic behavior under varying conditions. The obtained results demonstrate that the proposed analytical framework can effectively describe the temporal evolution of infectious diseases while preserving the mathematical structure of the original model. Owing to its flexibility and analytical nature, the proposed approach can serve as a useful tool for investigating infectious disease dynamics and may provide theoretical support for future studies in epidemiological modeling and health informatics.