Epidemic dynamics on semi-directed complex networks

- A new dynamical model is proposed to study the epidemic spreading on semi-directed networks.
- We obtain the outbreak threshold on semi-directed networks.
- If R0>1, then the unique endemic equilibrium exists and is globally asymptotically stable.
- Mathematically, a new high dimensional system has been established and partly analysed.

In this paper an SIS model for epidemic spreading on semi-directed networks is established, which can be used to examine and compare the impact of undirected and directed contacts on disease spread. The model is analyzed for the case of uncorrelated semi-directed networks, and the basic reproduction number R0 is obtained analytically. We verify that the R0 contains the outbreak threshold on undirected networks and directed networks as special cases. It is proved that if R0<1 then the disease-free equilibrium is globally asymptotically stable, otherwise the disease-free equilibrium is unstable and the unique endemic equilibrium exists, which is globally asymptotically stable. Finally the numerical simulations holds for these analytical results are given.