Analysis of a Compartmental Model for <i>Norovirus</i> Transmission Through Environmental Contact

Norovirus remains a leading cause of acute gastroenteritis globally, posing substantial public health and economic challenges. This study introduces a mathematical model to examine Norovirus transmission dynamics in environmental settings, incorporating time‐dependent control parameters including isolation of symptomatic individuals and environmental sanitation measures. The model establishes both disease‐free and endemic equilibrium points with analytical characterization of their existence conditions. Global asymptotic stability of the disease‐free equilibrium is demonstrated using linear Lyapunov functional analysis when the control reproduction number R c &lt; 1, while endemic equilibrium stability is analyzed through quadratic Lyapunov functions. Optimal control strategies are characterized via Pontryagin’s maximum principle to minimize infection burden while balancing intervention costs. Sensitivity analysis reveals that environmental transmission rates and hygiene interventions are the most influential parameters for controlling Norovirus outbreaks, with the recruitment rate of susceptible individuals serving as a primary driver of transmission potential. Cost analysis demonstrates that environmental sanitation measures achieve superior cost‐effectiveness when implemented individually, while isolation controls provide limited effectiveness without complementary environmental interventions. Numerical simulations illustrate the population dynamics and validate the effectiveness of integrated control approaches that prioritize environmental decontamination. The findings provide quantitative insights into Norovirus transmission dynamics and support evidence‐based design of economically viable intervention strategies for outbreak management in institutional settings.