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Allee effects in a discrete-time host-parasitoid model with stage structure in the host
We study a single-species population model with two stages,
adults and juveniles, and the model with Allee effects. In these
models, the fertility rate of an adult individual is assumed to be
density dependent on the total adult population size and the
transition probability from juvenile to adult over each time unit
is assumed to be a constant. Both models exhibit a boundary
$2$-cycle. Population persistence can occur for the model without
the Allee effects. However, there exists a population threshold
below which the population will go to extinction if the Allee
effects are considered. We also propose a host-parasitoid model
with stage structure in the host. Both populations can coexist
with each other under some conditions if Allee effects are
ignored. On the other hand, there exists a host population
threshold below which both populations become extinct if Allee
effects are incorporated into the interaction.