Flatten the curve

Nonlinear known dynamics — a compartmental SIR model — with a non-pharmaceutical intervention u that scales transmission, beta -> beta*(1-u). Optimal control holds infections at a hospital-capacity threshold with minimal intervention, the threshold a steep penalty rather than a hard limit: optimal control on a classic nonlinear population model, differentiating through the rollout. In observational logs the intervention's effect would be confounded, because policy reacts to case counts; here the plant is the true system and control is planned against it.

uv run python scripts/epidemic_demo.py

What it printed when this site was built:

capacity I_max      = 0.100
uncontrolled peak I = 0.536   (overshoots capacity)
controlled peak I   = 0.101   (flattened to capacity)
total NPI effort    = 43.84,  max u = 0.80
wrote outputs/epidemic.png

With matplotlib installed the script also writes outputs/epidemic.png; tutorial 4 draws the curves. Code: chc.epidemic.