2011/12/20 by Tom Britton, Britton, Tom, David Lindenstrand +1
Computer Science · Mathematics · Physics and Astronomy · #60 #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Probability (math.PR) #Social and Information Networks (cs.SI) #cs.SI #math.PR #msc:60 #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.1112.4718
arxiv created 2011/12/20 · arxiv updated 2011/12/21
A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such that individuals are heterogeneous in terms of how susceptible and infectious they are. The basic reproduction number R0 is derived and studied for various examples, but also the size and probability of a major outbreak. The qualitative conclusion is that R0 gets larger as the community becomes more heterogeneous but that different heterogeneities (degree distribution, weight, susceptibility and infectivity) can sometimes have the cumulative effect of homogenizing the community, thus making R0 smaller. The effect on the probability and final size of an outbreak is more complicated.