Dynamics and equilibrium conditions of density-dependent-limited populations under RIDL/SIT control. We compared the effectiveness of SIT (blue line) and a late-acting lethal RIDL strategy (thick red line) in a mathematical model of a continuous breeding Ae. aegypti population limited by density-dependent mortality (for details of the model see Methods). The population is assumed to start at equilibrium carrying capacity, and will therefore remain at the initial level if there is no intervention (black line). All releases are assumed to be of males only; the input release ratio, I, is defined relative to the initial wild male population; this rate of release of males then remains constant through time. In panels A and B, we plotted examples of the variation over time, from the start of control, of the number of females in the population relative to the initial number, for two different release ratios. The RIDL insects are assumed to be homozygous for a construct lethal to males and females ("non-sex-specific") after the density-dependent phase. For conventional SIT, mortality is assumed to be early (at embryogenesis), before any density-dependent mortality operates. With a low release ratio (A), SIT can actually increase the equilibrium size of the adult female population while RIDL can result in eradication. With a sufficiently high release ratio (B), conventional SIT can control the population, but the RIDL strategy is more effective. In panels C, D, E and F, we plot the equilibrium number of female mosquitoes in the population, relative to the initial numbers, following control with a given input ratio. The critical input ratios required to achieve eradication are shown as broken lines for the conventional SIT (blue) and RIDL systems (red). β represents the intensity of the density-dependence; P is the maximum per capita daily egg production rate corrected for density-independent egg to adult survival (see Methods). Parameter values for β and P (indicated in the panels) represent the best-estimate ranges calculated by Dye for a natural Ae. aegypti population . In all cases, T = 27 days and δ = 0.12 per day; parameter values again taken from Dye .
Phuc et al. BMC Biology 2007 5:11 doi:10.1186/1741-7007-5-11