Substance Adoption

SD · 39

SUR contagion model. dS/dt = −βSU/N + ωRc; dU/dt = βSU/N − ρU; dRc/dt = ρU − ωRc. Reinforcing peer infection drives S-curve uptake; recovery and relapse set the long-run equilibrium.

peer factor β 0.45

recovery rate ρ 0.10

relapse rate ω 0.05

initial users U₀ 1

t (months)0

Susceptible S—

Users U—

Recovered Rc—

R₀ ≈ β/ρ—

peak U%—

SusceptibleUsersRecovered