Each of the 1,200 dots on the disc is one person in a synthetic cohort. Every person keeps a fixed random susceptibility u ∈ [0,1] drawn once at start; a person smokes whenever u is below the population's current smoking prevalence P(t). Since u is uniform, exactly a fraction P(t) of dots are lit red at every moment — and because susceptibility is fixed per-person, the same low-u individuals are always the last to quit, a reasonable stand-in for addiction severity. Dots are laid out with the same golden-angle phyllotaxis spiral (θᵢ = i·π(3−√5), r ∝ √i) used to pack sunflower seeds and pine cones evenly across a disc — the genuine 2D counterpart of the 3D sibling's Fibonacci-sphere cloud, not a flattened projection of it.
P(t) itself follows a standard stock-and-flow (compartmental) model used in tobacco-control policy simulators such as WHO's SimSmoke:
dP/dt = I(t)·(1 − P) − C(t)·P
I(t) = I0 · max(0, 1 − εI·τ) · (0.6 + 0.008·A)
C(t) = C0 · (1 + εC·τ) + kF · F/100
τ = excise tax rate (0–3.0, i.e. 0–300% of baseline price)
A = advertising exposure (0–100)
F = cessation-program funding ($/capita/yr, 0–100)
I0 = 0.03/yr baseline initiation, C0 = 0.05/yr baseline cessation
εI ≈ 0.5, εC ≈ 0.35 (price-elasticity coefficients), kF ≈ 0.10
P* = I / (I + C) ← the equilibrium the population is always relaxing toward
- Excise tax raises retail price; higher prices both deter new smokers (lower I) and push existing smokers to quit (higher C) — the WHO/Chaloupka literature puts overall cigarette price elasticity of demand around −0.4, with youth roughly 2–3× more price-sensitive than adults. Note the initiation term is clamped at zero: past τ = 2.0 (200% tax) the model's own max(0, …) floor means the tax can no longer suppress initiation further, only cessation keeps rising — a deliberate floor in the source model, reproduced here unchanged.
- Cessation funding only raises C — it helps people already smoking quit, without touching initiation.
- Advertising exposure only scales I — more marketing recruits more new smokers, independent of price.
- P(t) is integrated forward with a clamped time step, so the disc's red fraction and the live P(t) chart both visibly move toward the new equilibrium P* = I/(I+C) as you move the sliders.
This is a policy-elasticity teaching model, not a calibrated public-health forecast — but every term corresponds to a real, published lever used in national tobacco-control planning.