Hierarchical coarse-grained approach to the duration-dependent spreading dynamics on complex networks

Abstract

Abstract Various coarse-grained models have been proposed to study the spreading dynamics on complex networks. A microscopic theory is needed to connect the spreading dynamics with individual behaviors. In this letter, we unify the description of different spreading dynamics by decomposing the microscopic dynamics into two basic processes, the aging process and the contact process. A hierarchical duration coarse-grained (DCG) approach is proposed to study the duration-dependent processes. Applied to the epidemic spreading, such formalism is feasible to reproduce different epidemic models, e.g., the SIS and the SIR models, and to associate the macroscopic spreading parameters with the microscopic mechanism. The DCG approach enables us to study the steady state of the duration-dependent SIS model. The current hierarchical formalism can also be used to describe the spreading of information and public opinions, or to model a reliability theory on networks.