Functional Law of Large Numbers and PDEs for Spatial Epidemic Models with...
summary
Proves a functional law of large numbers for a non‑Markovian SIR model as both number of patches and individuals per patch → ∞, giving local‑uniform convergence in probability to coupled time‑space integral equations (not ordinary ODEs). Key tools are Poisson time‑change representations, martingale error estimates and tightness, and solving the age‑structured limit by characteristics to obtain a time‑age‑space integral equation (equivalently a PDE with a boundary term). Spatial coupling enters only through a graphon coupling kernel beta; mean‑field becomes exact in the limit.
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chapters (9)
- 0:00Introduction
- 1:04Spatial epidemic model overview
- 14:50Force of infection dynamics
- 21:39Finite population model
- 31:46Law of large numbers assumptions
- 37:36Deriving limiting equations
- 48:48PDE for infection age
- 58:01References
- 1:00:54Q&A
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