Each hive runs a real SIR compartmental model — Susceptible, Infected, Recovered bee populations — integrated with the standard nonlinear ODEs:
dS/dt = -β·S·I/N - Σⱼ (Cᵢⱼ·S/N)·Iⱼ
dI/dt = β·S·I/N + Σⱼ (Cᵢⱼ·S/N)·Iⱼ - γ·I
dR/dt = γ·I
The first term is within-hive transmission (Varroa/virus contact between nestmates); the summed term is cross-hive transmission carried by drifting or robbing foragers, with coupling Cij = K / distanceij — an inverse-distance law, so closer hives infect each other faster. Raising the hive-spacing slider stretches every distance in the layout and weakens every coupling term at once.
The basic reproduction number R₀ = β/γ is the textbook single-hive threshold: above 1 the infection grows exponentially in an isolated hive, below 1 it dies out. The network can still sustain an epidemic below that threshold if enough neighbouring hives keep reseeding each other through drift.
- Hive map — each circle is one hive; the fill mixes green (S), red (I) and blue (R) in proportion to its own compartments, radius scales with colony size, and lines between hives show active drift coupling (brighter = stronger).
- Epidemic curve — aggregate S/I/R fraction across the whole apiary network over time.