Epidemics on social network graphs
نویسنده
چکیده
This work is concerned with relaxing the assumption of homogeneous mixing in a Reed-Frost epidemic model. After a thorough presentation of the standard Reed-Frost model we introduce social structure in the population by aid of a social network graph and investigate the effects on the epidemic spread. A number of possible choices for the underlying social network are presented: Bernoulli graphs, 3-clique graphs, Markov graphs, Household graphs and small-world networks. For each of these structures we investigate if it can be regarded as a good model for a social network. We also derive asymptotic formulas for epidemiological quantities like the basic reproduction number and the final size of the epidemic. When exact results are beyond reach computer simulations are presented. Department of Mathematics, Stockholm University, SE-10691 Stockholm, Sweden.
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