A Mathematical Model in Public Health Epidemiology: Covid-19 Case Resolution Among Veterans Using Public-Use Surveillance Data and First-Order Differential Equations

Introduction: This project applies linear first-order differential equations to model COVID-19 case resolutions within the Veterans Health Administration. This model uses cumulative public health data to estimate case resolution, offering a practical tool for managing COVID-19 and potentially other communicable disease outbreaks. Methods: A two-part approach was adopted: Part A models cumulative COVID-19 recovery and death rates, while Part B incorporates vaccination data to refine these rates. The model is structured through first-order differential equations and a homogeneous mixing assumption, using a meticulously cleaned dataset to ensure accurate forecasting of disease outcomes across a healthcare system. Findings: In Part A, baseline rates (recovery=0.9717, death=0.0267) provided a control for assessing vaccination impact. With cumulative vaccination data, in Part B, vaccination-adjusted rates showed enhanced recovery (1.5066) and reduced death (0.0193). This model uses public-use, cumulative public health surveillance data, enabling real-time adaptations with minimal computational complexity. Discussion: We demonstrate that vaccination increases COVID-19 recovery rates and reduces mortality within a public healthcare system. Using a differential equation model with validated data protocols, this approach combines mathematical rigor and data integrity with actionable insights, offering a reliable foundation for strategic public health decisions. Conclusion: COVID-19 case resolution in the Veterans Health Administration was modeled using a firstorder differential approach. Vaccination-adjusted recovery and death rates showed improved outcomes, supporting resource planning and related public health efforts. A consistency check validated the stability of the model across datasets, supporting its reliability in public health decision-making.