Activity of nodes reshapes the critical threshold of spreading dynamics in complex networks

• A model of spreading dynamics in complex networks with active nodes is proposed.
• Critical threshold of spreading dynamics is reshaped into a critical curve composed of critical infection rate and critical activity rate.
• Final size of spreading dynamic depends on both infection rate and activity rate.
• Decreasing of activity rate causes slowing down of spreading dynamics.

In this paper, we investigate spreading dynamics on complex networks with active nodes based on SIR (Susceptible–Infected–Removed) model. Different from previous studies, each node of the network rotates between active state and inactive state according to certain probabilities. An active susceptible node can be infected by all its infected neighbors, while an inactive susceptible node can only be infected by its active infected neighbors. By means of ​mean-field approach and numerical simulations, we explore the critical phenomenon by the combined effects of activity rate and infection rate on spreading dynamics. We show that the critical threshold of infection rate is increased by node activity, and node activity also shows a critical phenomenon given certain infection rate. On the whole, there exists a critical curve consists of pairs of critical activity rate and infection rate. We also analyze theoretically the impact of activity rate and infection rate on the final size of spreading dynamics, which is verified by numerical simulations. This work complements our understanding of spreading dynamics with active nodes and may be used to develop more feasible and more economical methods to control spreading dynamics.