Integration of Developed Mathematical Model for Predicting and Monitoring the Spread of Epidemics and Pandemics: The Case of COVID-19 in Rwanda.

This study presents a novel, context-specific mathematical modeling framework for predicting and monitoring COVID-19 transmission in Rwanda, addressing the increasing demand for integrated and data-driven public health decision-support tools. The model incorporates localized epidemiological dynamics, transmission pathways, and major intervention measures, including lockdowns, vaccination, quarantine, and home-based care, which is considered a critical factor influencing disease transmission. Using a system of differential equations, the framework models transition among infected, home-based care, hospitalized, recovered, and deceased populations. The model was calibrated and validated using Rwanda's national COVID-19 surveillance data collected between March 2020 and December 2022, covering multiple epidemic waves and intervention phases. Calibration utilized time-series data on confirmed cases, active infections, hospitalizations, intensive care unit admissions, recoveries, and mortality. Detailed home-based care records improved the estimation of transmission and recovery parameters. Parameter optimization was performed through least-squares fitting and cross-validation techniques. Model performance was assessed using the root mean square error (RMSE) and the coefficient of determination (R 2) metrics. Validation through out-of-sample predictions demonstrated strong accuracy in capturing infection trends and healthcare burden. An interactive dashboard complements the framework by enabling real-time analytics, forecasting, and evidence-based public health decision-making.