An Extended Mathematical Model of COVID 19 Transmission Incorporating Healthcare Worker Exposure, Environmental Contamination and Healthcare System Stress

This study presents an extended mathematical model for COVID-19 transmission that incorporates interactions between healthcare workers, non-healthcare workers, environmental contamination, and personal protective equipment (PPE) effectiveness under healthcare system stress. The model is formulated as a system of ten nonlinear differential equations and analyzed to establish positivity, boundedness, and the existence of disease-free and endemic equilibria. The control reproduction number is derived using the next-generation matrix method, and local and global stability properties of the equilibria are investigated. A normalized forward sensitivity analysis identifies the most influential parameters driving transmission dynamics. Using Nigeria-specific parameter values, numerical simulations are conducted to illustrate the model behavior and validate the analytical results. The findings reveal that community transmission, healthcare worker exposure, PPE availability, and environmental contamination play critical roles in sustaining COVID-19 transmission. The model provides quantitative insight into the effectiveness of integrated intervention strategies and offers a useful framework for guiding public health policy in resource-constrained settings such as Nigeria.