The science
Model (per study area, units kg and days)
dC/dt = I − V·f(C) − d(T)·C, where I = λ·200 kg is carrion input. Vultures remove carrion with a Holling type II functional response f(C) = fmax·C/(Ch + C): each bird eats at most fmax = 1.2 kg/day, half-saturating at Ch = 40 kg. Microbes and insects decompose carrion at d(T) = d20·Q10(T−20)/10, with d20 = 0.15/day and Q10 = 2.
Vulture numbers
dV/dt = r·V·(f/fm − 1) − μ·V with r = 0.01/day and a maintenance intake fm = 0.6 kg/day; positive growth is limited by a territory cap K = 400 (factor 1 − V/K); μ is the extra mortality (e.g. poisoned carcasses). Real vulture demography is much slower (low breeding rate), so the speed slider compresses years into seconds. Parameter values are plausible round numbers, not measurements of one species.
Disease-risk index (illustrative)
Carrion that lingers feeds bacteria and flies and brings in mammalian scavengers. We show residence time τ = C/I (Little's law) and an exposure total ∫C·Q10(T−20)/10 dt /1000 in arbitrary units. It is an index for comparing scenarios, not an epidemiological prediction.
Independent check
For fixed V the steady state solves d·C² + (V·fmax + d·Ch − I)·C − I·Ch = 0, C* = [−b + √(b² + 4·d·I·Ch)]/(2d), b = V·fmax + d·Ch − I. The experiments integrate the differential equation with RK4 and compare with this formula.
Real-world context
In India in the 1990s–2000s some vulture species fell by more than 95% after the veterinary drug diclofenac got into carcasses (widely reported); feral dog numbers and human rabies risk are linked in the literature. This toy model shows the mechanism in outline only.