A Caputo fractional-order model for norovirus transmission with vaccination and environmental reservoir

Abstract

This study develops a Caputo fractional-order compartmental model to analyze norovirus transmission dynamics by explicitly incorporating vaccination and environmental reservoirs. Unlike classical integer-order models that neglect memory effects, the proposed model captures memory-dependent transmission mechanisms that are essential for describing norovirus persistence and recurrent outbreaks. The population is divided into seven compartments: susceptible, vaccinated, exposed, symptomatic, asymptomatic, recovered, and pathogen-contaminated environment. Using fractional derivatives of order 0 < α ≤ 1 , the model accounts for historical effects in disease progression and environmental contamination. The analytical results establish the positivity, boundedness, and existence of unique solutions. The effective reproduction number R e is derived using a Next-Generation Matrix approach, and stability conditions for both the disease-free and endemic equilibria are obtained under fractional-order dynamics. Numerical simulations show that lower values of the memory parameter α slow outbreak progression and prolong infection persistence, while increased vaccine efficacy and public health interventions significantly reduce infection prevalence. Higher environmental shedding rates sustain transmission and delay disease elimination. These results demonstrate that integrating memory effects, vaccination strategies, and environmental contamination provides a more accurate framework for norovirus outbreak modeling and control. • Develops a fractional-order model capturing memory-dependent norovirus transmission. • Integrates vaccination, behavioral interventions, and environmental reservoirs. • Provides analytical results: positivity, boundedness, reproduction number, and stability. • Shows via simulations the effects of memory, vaccination, and environmental shedding. • Lays groundwork for optimal control and cost-effective intervention strategies.