Modeling the adaptive behavior of an agricultural pest population

Abstract

In this work, we formulate a model describing the growth of a pest population with seasonal diapause at the larval stage. The model includes the insect resistance to chemical treatments and their adaptation against a hostile environment. It consists on the description of three classes: the immature stage that includes eggs, larvae and pupae, and two mature stages corresponding to the vulnerable adult stage and the insecticide resistant adult stage. The main result consists in an analytical approach for the existence of a nonnegative periodic solution. The proof uses comparison results and Kamke's Theorem for cooperative systems. As an important illustration, a threshold type result on the global dynamics of the pest population is given in terms of an index R. When R≤1, the trivial solution is globally asymptotically stable. When R>1, the positive periodic solution is globally asymptotically stable. Numerical simulations confirm the analytical results.