Worker bees carry foraged tree resin back to the hive and mix it with wax to make propolis, which they pack into every crack and seam in the hive wall — the "propolis envelope". This lab models that process directly instead of showing decorative resin blobs:
closure_rate(gap) = n_assigned(gap) · resinRate / K [mm/s]
open_fraction(t) = ΣopenWidth(t) / wallLength
intrusion_rate = β · open_fraction [pathogens/min]
heat_loss = ΔT·[open_fraction·U_gap + (1-open_fraction)·U_propolis] [W/m²]
Each open gap is assigned a share of the active workforce; every assigned bee closes its gap at a rate set by how fast it can collect and deposit resin (resinRate) divided by the resin mass needed per millimetre of closure (K, fixed). When a gap seals, its bees are reassigned to the next open gap, so more workers or a faster collection rate directly shortens sealing time.
- Pathogen intrusion rate — an epidemiological-style exposure model: the rate pathogens cross the wall is proportional to the open-gap area exposed to the outside, exactly like a "force of infection" term proportional to exposed surface. It falls as sealing proceeds.
- Heat loss — open cracks conduct heat far faster than packed propolis (U_gap ≫ U_propolis), so wall heat loss is a weighted average of open and sealed conductances, weighted by open_fraction — it falls in lock-step with the same coverage metric that drives the pathogen curve.
- Insulation gain — 1 − open_fraction, the fraction of the wall's original heat-loss pathway that propolis has closed off.