Spatial dynamics of a pest population with stage-structure and control

We study an integro-difference model for a pest population that is divided into four life stages. In the model, spatial spread of the population is described by an integral convolution and pest control is applied to each population stage. When the spatial domain is infinite, we establish the spreading speeds and existence of traveling waves; when the spatial domain is finite, we first establish threshold conditions in terms of the principal eigenvalue of an associated eigenvalue problem to determine population persistence and extinction, and then define the net reproductive rate and use it to develop equivalent threshold conditions for persistence and extinction. The cases where the reproduction function is monotone and where it is nonmonotone are both investigated. Numerical simulations show that the larger the control effectiveness is the easier to eradicate the pest population and that the same control effectiveness on different stages may yield different population dynamics in the long-term.