Effect of overlap on spreading dynamics on multiplex networks

In spite of the study of epidemic dynamics on single-layer networks has received considerable attention, the epidemic dynamics on multiplex networks is still limited and is facing many challenges. In this work, we consider the susceptible-infected-susceptible-type (SIS) epidemic model on multiplex networks and investigate the effect of overlap among layers on the spreading dynamics. To do so, we assume that the prerequisite of one $S$-node to be infected is that there is at least one infectious neighbor in each layer. A remarkable result is that the overlap can alter the nature of the phase transition for the onset of epidemic outbreak. Specifically speaking, the system undergoes a usual continuous phase transition when two layers are completely overlapped. Otherwise, a discontinuous phase transition is observed, accompanied by the occurrence of a bistable region in which a disease-free phase and an endemic phase are coexisting. As the degree of the overlap decreases, the bistable region is enlarged. The results are validated by both simulation and mean-field theory.