Epidemic Models: Their Spread, Analysis and Invasions in Scale-Free Networks

The mission of this chapter is to introduce the concept of epidemic outbursts in network structures, especially in case of scale-free networks. The invasion phenomena of epidemics have been of tremendous interest among the scientific community over many years, due to its large scale implementation in real world networks. This chapter seeks to make readers understand the critical issues involved in epidemics such as propagation, spread and their combat which can be further used to design synthetic and robust network architectures. The primary concern in this chapter focuses on the concept of Susceptible-Infectious-Recovered (SIR) and Susceptible-Infectious-Susceptible (SIS) models with their implementation in scale-free networks, followed by developing strategies for identifying the damage caused in the network. The relevance of this chapter can be understood when methods discussed in this chapter could be related to contemporary networks for improving their performance in terms of robustness. The patterns by which epidemics spread through groups are determined by the properties of the pathogen carrying it, length of its infectious period, its severity as well as by network structures within the population. Thus, accurately modeling the underlying network is crucial to understand the spread as well as prevention of an epidemic. Moreover, implementing immunization strategies helps control and terminate theses epidemics.