Coupled dynamics of SIRS-UAU disease-awareness spreading on multiplex networks

In this paper we investigate an SIRS-UAU disease-awareness spreading model on multiplex networks that incorporates the influence of mass media. Through the microscopic Markov chain approach, we derive the evolution equations for the probability of an individual being in each possible state and obtain the epidemic threshold, which is shown to be a continuous phase transition point between the disease-free state and the endemic state in the phase diagram. Our results show that increasing the immunity wanning rate will enlarge the epidemic prevalence and reduce the fraction of recovered individuals; however, the temporal immunity has no impact on the epidemic threshold. Moreover, implementing mass media broadcast helps raise the awareness incidence and decrease the fraction of recovered individuals. In addition, for the special case when awareness confers complete self-protection against infection, the mass media broadcast significantly diminishes the epidemic prevalence and increases the epidemic threshold. Nevertheless, when awareness provides only partial self-protective effectiveness, the mass media broadcast plays a limited role in changing the epidemic prevalence and the epidemic threshold. Furthermore, in the special case where the mass media broadcast is not included, we discover the metacritical point, a point above which the epidemic threshold starts to grow nonlinearly with the awareness spreading rate and below which the epidemic threshold is independent of the awareness spreading rate. Conversely, the metacritical point disappears as long as the mass media broadcast is incorporated into the model. Our analytical results are confirmed by extensive Monte Carlo simulations.