Development and Analysis of Models for the Spread and Control of Weeds and Infectious Diseases

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Allen 9626417 The goals of this research involve two different but related biological areas; one area is weed control and the other is control of infectious diseases. By their very nature, weeds and infectious disease agents are unwanted invaders in a host system; their introduction frequently has adverse effects. Practical methods for control of weeds and infectious diseases are under continual research and development. However, there is a need for theoretical justification and predictability of these control procedures. This project develops and analyzes mathematical models that provide quantitive and qualitative means for evaluation of these control procedures. Integrodifference equations provide a realistic starting point for modeling the biological dynamics of these two processes; the time variable is discrete but the spatial and state variables are continuous. Discrete-time models describe plant populations whose generations are nonoverlapping and epidemics where the observation of cases or the seasonal movement and population densities of animals relate to the discrete time interval. Mathematical models for weeds and infectious diseases are analyzed to determine the effects of spatial dispersal, age or stage structure, multi-population interactions, and general growth assumptions on model behavior. Two important questions are addressed: (i) How fast does the weed or disease spread? and, (ii) What are the short- and long-term effects of a control procedure? Determining effective control procedures for weeds and infectious diseases has become a significant global environmental problem. Around the world, native plant communities are being displaced by nonnative plants and enzootic wildlife diseases are becoming a threat to humans. In particular, agricultural land and rangeland, where the native plant community structure has been altered, are especially vulnerable to invasions by introduced plant species. Humans living in close proximity to an animal reservoir of a disease are at an increased risk of contracting the disease. It is the goal of this research to apply the mathematical models and theoretical techniques that are developed in this project to two important and timely biological problems: (1) control of weeds in agricultural fields or rangeland and (2) control of rabies in wildlife populations. Formulation, analysis, and numerical simulation of mathematical models provide a greater understanding of effective methods for the control of the spread of weeds in fields or rangeland and of rabies in wildlife. Various control strategies are compared to determine the most effective short- and long-term strategies that prevent or reduce the spread while causing minimal damage or change to the environment and minimal risk to humans.