Beekeeping Skill Adoption — Bass Diffusion Network

Learner Network

Days per second 3.0

Innovation p 0.030

Imitation q 0.38

Learners N 120

Cohort

Day

Adopted

0/0

F(t) sim

New today

Solid gold line is this run's stochastic network adoption; dashed line is the exact closed-form Bass solution for the same p, q — they should track each other closely.

How it works

Each learner sits in a small-world peer network (a ring lattice of local peer links, plus a handful of long-range rewired links standing in for online forums/social media). Every simulated day, every still-unskilled learner faces the same real Bass hazard rate — the probability of taking up beekeeping skills that day, driven by the course platform itself (p) plus word-of-mouth from everyone who has already adopted (q times the current adopted fraction F). Individual adoption events are drawn stochastically from that hazard, one learner at a time, so the network's own cumulative fraction is the true F(t) — not a separately-faked curve.

dF/dt = (p + q·F)·(1 − F)
hazard(day) = p + q·F(t)          [probability an unskilled learner adopts today]
F(t) = (1 − e^-(p+q)t) / (1 + (q/p)·e^-(p+q)t)   [closed-form solution, p,q > 0]

Innovation p — the rate learners adopt purely from the course platform itself (ads, the course listing, an article like this one) with no peer influence at all.
Imitation q — how strongly already-skilled peers pull the rest of the network in; a higher q makes the curve's characteristic S-shape steeper once adoption gets going.
Learners N — the market size: how many nodes make up the cohort network.
Days per second — how fast simulated time advances.

Real-world relevance: this is the same Bass model economists and course platforms use to forecast how a new online offering — a webinar series, a certification track — gets taken up by a population, with the p/q split telling them how much of their growth is marketing versus genuine word-of-mouth.

Unskilled Skilled Simulated F(t)