Sericea Lespedeza (Lespedeza cuneata), a perennial legume native to Asia, has been introduced in the United States for erosion control, providing forage to livestock and wildlife cover. It is drought tolerant, can grow in a range of soil types, and produces enormous amounts of seeds, which result in the establishment of the Sericea Lespedeza population very quickly. Native grasslands in the Great Plains are threatened by the spread of Sericea Lespedeza, which can damage forage or hay production leading to substantial economic costs to landowners. Sericea Lespedeza has been declared as a noxious weed by the state of Kansas. The current practice for controlling the growth of Sericea Lespedeza is by using herbicides. Although they are available, effective control can be expensive because of the scale of the problem and the necessity of repeated herbicide applications over many years to kill the new plants germinating from the long-lived seed bank. In this thesis, a dynamic nonlinear 0-1 integer programming model is developed to find economically efficient strategies to control the invasion of Sericea Lespedeza. Using empirical data, the model considers population growth rates, carrying capacity, seed dispersal, treatment costs, and economic loss due to invasion. The model minimizes the sum of damages to hay and forage due to the invasion of Sericea Lespedeza over time subject to two constraints: (1) the spread of invasive species over space and time, and (2) budget restricting the total cost of labor and herbicides used to prevent and control these invasive species. Finally, this thesis present results from different management scenarios as well as using various parameters considered in the model such as budget, dispersal rates, kill rates of the herbicides and initial infestation to provide insights regarding economically efficient strategies for controlling Sericea Lespedeza in the Great Plains.