A functional law of large numbers is proved for non-Markovian SIR epidemics with infection-age-dependent infectivity on large heterogeneous random graphs, with a graphon PDE as the limit.
SIR epidemics on evolving graphs
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abstract
We consider evoSIR, a variant of the SIR model, on Erd\H os-Renyi random graphs in which susceptibles with an infected neighbor break that connection at rate $\rho$ and rewire to a randomly chosen individual. We compute the critical infection rate $\lambda_c$ and the probability of a large epidemic by showing that they are the same for the delSIR model in which $S-I$ connections are deleted instead of rewired. The final size of a large delSIR epidemic has a continuous transition. Simulations suggest that the final size of a large evoSIR epidemic is discontinuous at $\lambda_c$.
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Stochastic heterogeneous SIR model with infection-age dependent infectivity on large random graphs
A functional law of large numbers is proved for non-Markovian SIR epidemics with infection-age-dependent infectivity on large heterogeneous random graphs, with a graphon PDE as the limit.