Fig 1.
Ordinary differential equation model of tsetse population dynamics.
Pupae, I, metamorphose into adults, V at rate β. We take ρ as the rate of production of pupae by adult females. Only half of the emerging flies are female, so female pupae are produced at rate ρ /2. Adult losses are due to background mortality at rate μb and starvation mortality at rate μf, both considered density independent. Pupal losses are divided between density-independent mortality γ, and density-dependent mortality with coefficient δ. All rates have units days-1.
Table 1.
Model parameter inputs.
Fig 2.
Numbers of hosts shot during the Nagupande experiment.
The numbers shot each month are modelled using Eq 1 –either modelling all data together with a constant kill rate throughout (dashed line), or assuming that the kill rate was higher during the first two months of the study (solid line). Assuming a growth rate (r) of 0.007 month-1 the model fitted to data for all months gave estimates of k1 = 2591 (2492–2693), k2 = 0.0794 (0.0027–0.0828). Excluding the first two months gave estimates of k1 = 1951 (1865–2041), k2 = 0.0657 (0.0621–0.0693) for month 12 onwards.
Fig 3.
Ordinary differential equation (ODE) model fits to the mean monthly number of tsetse caught during ox-baited fly-round, and estimated number of hosts during the Nagupande experiment.
Host numbers assumed constant prior to the start of hunting. Mean monthly catches of G. m. morsitans in the Nagupande area (closed circles) and at the control site in Lusulu (open circles) are plotted on a logarithmic scale. Model fit A: fitting both σ (daily probability of finding and feeding on a host, given one host present within a square of side 1 km area around the fly), and μb (adult background mortality rate). σ = 0.124 (0.123–0.125); μb = 0.0180 (0.0176–0.0183) days-1; log likelihood 2216. Model fit B: assuming no mortality due to starvation (σ = 1) and fitting only background mortality μb, 0.03697 (0.03696–0.03699) days-1; log likelihood 4694. Fits use the values for input parameters given in Table 1. Note that we here assume no movement of flies into and out of the experimental plot.
Fig 4.
Output from agent-based model (ABM) of tsetse population dynamics including starvation-dependent mortality.
Assuming δ = 0.00001, σ = 0.135 and μb = 0.011. Lines represent the means over 10 model runs. Model A: assuming movement of flies into and out of the experimental area, with flies moving a straight-line distance of 0.5 cells/ 250m per day in a random direction, sum of squared residuals– 43. Model B: assuming a closed system with no movement of flies into or out of the experimental area. Sum of squared residuals– 294. σ is the daily probability that a fly finds, and feeds on a host, given one host is present within a square of side 1 km around the fly.