Bees have no antibodies — instead two layers of defence run at once. Left scene: haemocytes (mobile phagocytes, cyan) patrol the haemolymph and engulf pathogens (red) on contact, while surviving pathogens keep dividing. The active-pathogen count follows predator-prey kinetics:
dP/dt = rP(1 − P/Pmax) − kHP
r = infection intensity, H = haemocyte count
k = per-haemocyte kill rate (immune response speed)
Raise infection intensity and pathogens (P) outrun haemocytes and climb toward Pmax; raise immune response speed (more/faster haemocytes, larger k·H) and the kHP term dominates, pulling P back down.
Right scene: social immunity in the hive — infected brood cells (purple) appear at a rate tied to infection intensity. Worker bees (amber) inspect cells continuously; hygienic behaviour sets the per-inspection probability of detecting and removing ("uncapping") an infected cell before the pathogen inside can complete its cycle, which is exactly the trait beekeepers select for in hygienic and varroa-sensitive-hygiene breeding lines.
- Infection intensity — pathogen growth/spawn rate r, and new-infection rate in the hive.
- Immune response speed — number and speed of haemocytes, i.e. the kill term kH.
- Hygienic behaviour — % chance a worker detects and removes an infected cell per inspection.