Optimal epidemic spreading on complex networks with heterogeneous waiting time distribution

• A susceptible–infected–susceptible model with heterogeneous waiting time distribution is proposed.
• A mean-field theory is generalized to analyze the model.
• The epidemic threshold is dependent on both the network topology and the waiting time distribution.
• There is an optimal waiting time distribution at which the epidemic threshold reaches its maximum value.

In this paper, the effects of heterogeneous waiting time on spreading dynamics is studied based on network-dependent information. A new non-Markovian susceptible–infected–susceptible (SIS) model is first proposed, in which node’s waiting time is dependent on its degree and may be different from each other. Every node tries to transmit the epidemic to its neighbors after the waiting time. Moreover, by using the mean-field theory and numerical simulations, it is discovered that the epidemic threshold is correlated to the network topology and the distribution of the waiting time. Furthermore, our results reveal that an optimal distribution of the heterogeneous waiting time can suppress the epidemic spreading.