On a Discrete-Time Networked SIV Model with Polar Opinion Dynamics

This paper investigates novel epidemic spreading problems under the influence of opinion evolution in social networks, where the opinions reflect the public health concerns toward the epidemic. A coupled bilayer network is proposed, where the epidemics propagate over several communities through a physical network layer while the opinions evolve over the same communities through a social network layer. Specifically, the epi-demic spreading process is described by a susceptible-infected-vigilant (SIV) model, which introduces opinion-dependent epi-demic vigilance state compared with classical epidemic models. Additionally, a polar opinion dynamics model is adopted on the social network, which incorporates the infection prevalence and human stubbornness into the opinion evolution. By introducing an opinion-dependent reproduction number, we provide the stability analysis of disease-free and endemic equilibria and derive sufficient conditions for their global asymptotic stability. Simulations are conducted to verify the theoretical results.