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.