Effects of Resource Limitations and Cost Influences on Computer Virus Epidemic Dynamics and Tipping Points

One of the most important assessment indicators of computer virus infections is epidemic tipping point. Although many researchers have focused on the effects of scale-free network power-law connectivity distributions on computer virus epidemic dynamics and tipping points, few have comprehensively considered resource limitations and costs. Our goals for this paper are to show that (a) opposed to the current consensus, a significant epidemic tipping point does exist when resource limitations and costs are considered and (b) it is possible to control the spread of a computer virus in a scale-free network if resources are restricted and if costs associated with infection events are significantly increased. 1. Introduction Research on the epidemic dynamics of computer viruses has increasingly incorporated Watts and Strogatz’s [1] description of small-world networks (characterized by tightly clustered connections and short paths between node pairs) and Barabási and Albert’s [2] insights regarding scale-free networks marked by power-law connectivity distributions. The list of researchers using network approaches to computer virus models and analyses also includes Kuperman and Abramson [3], Newman [4, 5], Newman and Watts [6], Pastor-Satorras and Vespignani [7–11], Watts [12], and X. Yang and L. X. Yang [13]. All of these investigators have noted that the topological properties underlying communication networks exert considerable influence on computer virus epidemic dynamics and spreading characteristics and support subtle analyses that non-network-directed approaches cannot. A central issue for researchers using a network analysis approach is whether or not tipping points exist when computer viruses are spread via the Internet [7–11, 14–17]. According to Pastor-Satorras and Vespignani [7–11], Internet-based viruses and worms do not have positive epidemic tipping points, other researchers of epidemic dynamics and tipping points in scale-free networks also consistently argue that, regardless of spreading capability, all Internet-based computer viruses have high probabilities of stability and survival [18–21]. Note that new computer viruses are constantly emerging on the Internet, but the majority disappear almost immediately, and a tiny minority achieve epidemic status. This observation serves as our motivation to take a more detailed look at daily interaction and communication process limitations among users of e-mail, instant messaging software, online social network platforms, USB flash drives, and smart phones rather than the topological power-law