Self-awareness control effect of cooperative epidemics on complex networks.

Coinfection mechanism is a common interacting mode between multiple diseases in real spreading processes, where the diseases mutually increase their susceptibility, and has aroused widespread studies in network science. We use the bond percolation theory to characterize the coinfection model under two self-awareness control strategies, including immunization strategy and quarantine strategy, and to study the impacts of the synergy effect and control strategies on cooperative epidemics. We find that strengthening the synergy effect can reduce the epidemic threshold and enhance the outbreak size of coinfected networks. On Erdős-Rényi networks, the synergy effect will induce a crossover phenomenon of phase transition, i.e., make the type of phase transition from being continuous to discontinuous. Self-awareness control strategies play a non-negligible role in suppressing cooperative epidemics. In particular, increasing immunization or the quarantine rate can enhance the epidemic threshold and reduce the outbreak size of cooperative epidemics, and lead to a crossover phenomenon of transition from being discontinuous to continuous. The impact of quarantine strategy on cooperative epidemics is more significant than the immunization strategy, which is verified on scale-free networks.