Residents are nodes on a real small-world social network (Watts–Strogatz: a ring lattice where each resident starts tied to their nearest neighbors, then a fraction of those ties are randomly rewired to distant residents — the same topology used to model how real word-of-mouth "small worlds" work). Each resident is unaware (grey), aware (blue) or practicing (green), and each carries their own adoption threshold drawn from a normal distribution (mean + spread, both tunable) representing how socially convinced they personally need to be.
f_i = (# of node i's actual graph neighbors already aware/practicing) / degree(i)
node i becomes aware this week if:
f_i ≥ threshold_i (Granovetter peer-threshold contagion), OR
rand() < p + q·f_i (Bass-style outreach + peer-influence probability)
node i (aware) becomes practicing this week if: rand() < r
Both rules run genuinely over the graph's real adjacency lists every simulated week — nothing here is scripted or pre-baked. The share of the community actually practicing drives a habitat-health index H that relaxes toward it with a lag, and the strip chart below the network plots the live, emergent adoption S-curve (aware share and practicing share vs. simulated weeks) as it is computed:
dH/dt = k · (F_practicing − H)
- External outreach p — baseline chance any unaware resident learns from the campaign directly, independent of neighbors.
- Peer influence q — how strongly a resident's informed neighbor share nudges the probabilistic outreach channel.
- Adoption threshold (mean/spread) — the population's distribution of how large a locally-informed neighbor share must be before a resident tips over on their own, per the threshold-contagion rule above.
- Practice adoption rate r — how fast an aware resident turns knowledge into sustained action.
- Launch Campaign Pulse — instantly informs a burst of residents scattered across the real graph, seeding new spread fronts.
This combines two textbook diffusion models — Granovetter threshold contagion and Bass innovation diffusion — computed over an explicit graph, the same class of model used to study how real environmental-education programs and conservation campaigns propagate through communities.