## Probability Seminar: Dong Yao, Duke

**Probability Seminar
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**Thursday, February 20th, 2020**

Hanes 125

4:15 PM

Hanes 125

4:15 PM

Dong Yao

**Duke University, Mathematics Department**

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**Epidemics on Evolving Graphs**

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The evoSIR model is a modification of the usual SIR process on a graph G in which S−I connections are broken at rate ρ 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 λ decreases to λc, 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 Δ determined by the first three moments of the degree distribution, so that the transition is discontinuous if Δ>0 and continuous otherwise.

**Refreshments will be served at 3:45 in the 3rd floor lounge of Hanes Hall**