Mathematical modeling of pest resistance to insecticides in a heterogeneous environment

Abstract

Insecticides are an effective tool for controlling grapevine moths such as Lobesia botrana. However, when massive use of insecticides, pests develop resistance because of selection of resistant individuals of the population and/or because of natural mutation. The main question is then to define a strategic pest management with respect to time and space. In the first part of this work, we present a model without spatial structure describing the dynamics of insects including its resistance to insecticides. In the second part, we include in the model dispersal between different space patches. Individuals can move from one patch to another at a fast time scale with respect to the demographical time scale. Using this model, we aim to understand the main characteristics leading to persistence or extinction of the insect pest population. We establish global stability results. Numerical simulations provide some interesting insights on the dynamics of the pest population.