Fractional-Order Analysis of Norovirus Transmission Dynamics With Optimal Control and Cost-Effectiveness

Norovirus remains a significant global public health challenge due to its high transmissibility, environmental persistence, and the absence of specific antiviral therapies or licensed vaccines. This study develops a novel Caputo fractional–order compartmental model (SEVIAR-B) to capture the transmission dynamics of norovirus, explicitly incorporating memory effects and environmental contamination. The fractional-order formulation provides a more accurate representation of long-term viral persistence, host immunity waning, and delayed intervention responses compared to classical integer-order models. Four time-dependent control measures personal hygiene (u1), vaccination (u2), treatment (u3), and environmental sanitation (u4) are integrated into the model to evaluate their epidemiological impact. Using Pontryagin’s minimum principle for fractional systems, the optimal control strategies were characterized and solved the resulting optimality system numerically. Nine distinct intervention combinations, ranging from single measures to comprehensive integrated approaches, are systematically compared. A rigorous cost-effectiveness analysis (CEA) based on the incremental cost-effectiveness ratio (ICER) is performed to identify economically optimal strategies under resource constraints. Our findings demonstrate that while comprehensive strategies (all controls active) achieve maximal infection reduction, the combined implementation of personal prevention, treatment, and environmental sanitation (Strategy F) provides the most favorable balance between public health impact and economic efficiency. This integrated framework offers a robust decision-support tool for evidence-based norovirus control policy formulation.