DYNAMICS OF DELAYED NICHOLSON’S BLOWFLIES MODELS

The extinction and the persistence of the population of the harmful sheep blowfly (Lucilia cuprina) are discussed in this paper through a stochastic mathematical model. Using appropriate Lyapunov functionals, the extinction of these flies depends on the time to oviposition and the time between generations. The oviposition period must be sufficiently short. Another species of blowfly, called Lucilia sericata, also attacks sheep in many areas. Both blowflies are ectoparasites of warm-blooded vertebrates, particularly domestic sheep. These two blowflies are related to sharing the same mitochondrial DNA sequences, although the two species are distinct. A sufficiently small egg-laying delay then leads to the rapid extinction of both blowfly populations.