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This paper is concerned with the growth rate of SIR(Susceptible-Infectious-Recovered) epidemics with general infectious perioddistribution on random intersection graphs. This type of graph is characterizedby the presence of cliques (fully connected subgraphs). We study epidemics onrandom intersection graphs with a mixed Poisson degree distribution and showthat in the limit of large population sizes the number of infected individualsgrows exponentially during the early phase of the epidemic, as is generally thecase for epidemics on asymptotically unclustered networks. The Malthusianparameter is shown to satisfy a variant of the classical Euler-Lotka equation.To obtain these results we construct a coupling of the epidemic process and acontinuous-time multitype branching process, where the type of an individual is(essentially) given by the length of its infectious period. Asymptotic resultsare then obtained via an embedded single-type Crump-Mode-Jagers branchingprocess.

The real-time growth rate of stochastic epidemics on random intersection graphs