TARGETED TREATMENT IN A COMMUNITY MODEL

Pesticides are essential in maintaining high crop yields, but they pose a threat to human health, the environment, and the sustainability of agriculture if used unwisely. Ideally, the amount of pesticide used would be minimized while keeping the same level of crop protection. Devising and testing new and efficient pest control strategies are costly and time consuming. Mathematical models and computer simulations offer a useful preliminary method of evaluating such control strategies. They are inexpensive and can incorporate the complex details of a farm's ecosystem.

Here a mathematical model is analyzed to study how redistributing pesticides among agricultural fields can increase pesticide efficacy. We model the spread of a pest from plant to plant like an infection through a population. The population of plants is partitioned into fields called communities where the pest can spread quickly and slowly jump from one community to another. Each community receives treatment (pesticide) which removes the pest. Instead of uniformly treating every community, we investigate targeted treatment where highly infected communities proportionally receive more treatment. The purpose of targeting is to increase the efficacy of treatment by applying it where it is most needed. Using analysis and computer simulation we show that although the endemic density of pests does not change after targeting is implemented, it slows the population's overall infection rate. Also, targeted treatment increases the likelihood of the pest population dying out due to random fluctuations when pest densities are low.