Epidemics 2

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" summary

Standard stochastic SIR on N individuals is shown to couple to a branching process by constructing IID Poisson contact processes, IID infectious periods and IID uniforms; the coupling holds with probability →1 up to about square-root-N coupling window, because ghost events (re-contacts) are unlikely. For Markovian infections the main phase follows a density-dependent jump Markov/Kurtz limit (deterministic SIR) with Gaussian O(1/√N) fluctuations, final size is either negligible or a fraction τ (Reed–Frost maximizes major-outbreak probability), and total duration scales like constants times log N.

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" chapters (7)

1. 0:00Start
2. 7:40Assumptions
3. 31:20Construction of the Branching Process
4. 44:44Ghost Event
5. 1:02:03Bivariate Process
6. 1:02:46Possible Events for Our Epidemic
7. 1:14:57Mean of a Poisson Process