Nonlinear Dynamics and Optimal Control Strategies of a Fractional-Order Norovirus Transmission Model

Abstract

Norovirus remains a highly contagious cause of acute gastroenteritis, characterized by rapid transmission and significant environmental persistence. In this study, we develop and analyze a fractional-order epidemiological model based on the Caputo derivative to describe Norovirus dynamics incorporating both direct human-to-human transmission and indirect environmentally mediated infection. The proposed model partitions the infected population into symptomatic and asymptomatic classes, each contributing differently to environmental viral shedding, while a dynamic environmental compartment captures viral accumulation and decay. The fractional order parameter \(\vartheta\) quantifies the strength of memory effects in transmission dynamics. We investigate the non-negativity and boundedness of solutions, derive the basic reproduction number \(R_0\) , and determine local and global stability conditions for disease-free and endemic equilibria. Sensitivity and bifurcation analyses identify key parameters governing outbreak persistence, particularly the environmental transmission rate and asymptomatic shedding contributions. An optimal control framework is introduced to assess the effectiveness of vaccination, treatment, sanitation strategies, and support the achievement of Sustainable Development Goal (SDG) 3. Numerical simulations demonstrate that combining environmental control with reduction of direct transmission significantly shortens outbreak duration. Overall, the results of the work represent an attempt to better understand environmentally mediated Norovirus transmission and help designing targeted intervention strategies.