Graphs with specified degree distributions, simple epidemics, and local vaccination strategies

Citation
Britton, Tom et al., Graphs with specified degree distributions, simple epidemics, and local vaccination strategies, Advances in applied probability , 39(2), 2007, pp. 922-948
ISSN journal
00018678
Volume
39
Issue
2
Year of publication
2007
Pages
922 - 948
Database
ACNP
SICI code
Abstract
Consider a random graph, having a prespecified degree distribution F, but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose that one individual in the community is externally infected by an infectious disease and that the disease has its course by assuming that infected individuals infect their not yet infected friends independently with probability p. For this situation, we determine the values of R0, the basic reproduction number, and .0, the asymptotic final size in the case of a major outbreak. Furthermore, we examine some different local vaccination strategies, where individuals are chosen randomly and vaccinated, or friends of the selected individuals are vaccinated, prior to the introduction of the disease. For the studied vaccination strategies, we determine Rv, the reproduction number, and .v, the asymptotic final proportion infected in the case of a major outbreak, after vaccinating a fraction v.