Discrete-Time vs. Continuous-Time Epidemic Models in Networks

Epidemic models have been a widely used mathematical tool in network security and social networks to study malware propagation and information dissemination. However, the relationships and the differences of discrete-time and continuous-time epidemic models in networks have not been systematically studied yet. In this paper, we focus on the susceptible-infectious model and attempt to connect and compare different discrete-time and continuous-time epidemic models through both theoretical analysis and empirical verification. We find that epidemic models can be distinguished based on whether a model considers the following three key factors: time intervals, spatial dependence among nodes, and linearization. We theoretically and empirically show that ignoring time intervals, assuming spatial independence among nodes, or applying linearization can cause a model to possibly over-predict the propagation speed of an epidemic. Especially, we discover that a widely used continuous-time epidemic model cannot accurately characterize the spread of the actual epidemic by ignoring both time intervals and spatial dependence among nodes.