The Effect of Herbicide Use on the Monarch Butterfly's (Danaus Plexippus) population dynamics

The Monarch Butterfly's annually migrates from central Mexico to southern Canada. Its population has been reduced during the recent decades, due to human interactions with their habitat. We examine the effect of herbicide usage on the Monarch Butterfly populationby creating a system of non-linear ordinary differential equations that describes the interaction between the monarch population and its environment at various stages of migration: spring migration, summer breeding and fall migration. The various stages of the model are used to describe the dynamic of population of multiple generations of adult Monarch Butterfly and larvae during spring migration. A predator-prey mathematical model with age's structure and three classes (larvae, adult, milkweed) is adopted to model the population dynamics at the summer breeding site. An exponential decay function is proposed to model the Monarch Butterfly's fall migration to central Mexico. The model is analyze to study the long-term behavior of the multi-stage system through numerical analysis, given data available i the research literature