A discrete-time networked SIS model with stubborn communities: the equilibrium analysis

This paper studies the discrete-time networked SIS (susceptible-infected-susceptible) model coupled with the opinion dynamics, where both the recovery rate and the infection rate are affected by the evolution of the opinions toward the epidemic. We consider that n communities are divided into non-stubborn communities and stubborn communities whose opinions remain unchanged. By analysing the existence and uniqueness of the system equilibria (i.e. the healthy state and the endemic state), and their stability, we find that the epidemic outbreak and eradication can be affected by the stubborn communities' opinions. Compared with the networked SIS model where opinions only affect their infection rates, we find that their endemic level is greater than or equal to the endemic level of our proposed model. Moreover, we analyse the effect of the stubborn communities' opinions on the endemic level. Finally, we illustrate the results through simulations.