Probability Seminar
Thursday, March 5, 2020, 4:15pm, at UNC, 125 Hanes Hall
Dong Yao (Duke, math)
Epidemics on Evolving Graphs

Abstract:

The evoSIR model is a modification of the usual SIR process on a graph $G$ in which $S-I$ connections are broken at rate $\rho$ and the $S$ connects to a randomly chosen vertex. The evoSI model is the same as evoSI but recovery is impossible. In a 2018 DOMath project the critical value for evoSIR was computed and simulations showed that when $G$ is an Erd\"os-Renyi graph with mean degree 5 the system has a discontinuous phase transition, i.e., as the infection rate $\lambda$ decreases to $\lambda_c$, the final fraction of infected individuals does not converge to 0. In this paper we study evoSI and evoSIR dynamics on graphs generated by the configuration model. We show that for each model there is a quantity $\Delta$ determined by the first three moments of the degree distribution, so that the transition is discontinuous if $\Delta>0$ and continuous if $\Delta<0$. We can also compute the limiting epidemic size in the supercritical regime. In evoSI there is a formula. In evoSIR we have to numerically solve a pair of ODE.

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