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

Allen 9626417这项研究的目标涉及两个不同但相关的生物学领域；一个是杂草控制，另一个是传染病控制。就其本质而言，杂草和传染病病原体是宿主系统中不受欢迎的入侵者；它们的引入往往会产生不良影响。控制杂草和传染病的实用方法正在不断研究和开发中。然而，这些控制程序需要理论证明和可预测性。本项目开发和分析数学模型，为评价这些控制程序提供定量和定性的手段。积分差分方程为这两个过程的生物动力学建模提供了一个现实的起点；时间变量是离散的，而空间变量和状态变量是连续的。离散时间模型描述的是世代不重叠的植物种群，以及与离散时间间隔相关的病例观察或季节性运动和动物种群密度的流行病。对杂草和传染病的数学模型进行了分析，以确定空间扩散、年龄或阶段结构、多种群相互作用和一般生长假设对模型行为的影响。解决了两个重要问题：(i)杂草或疾病传播的速度有多快？（ii）控制程序的短期和长期影响是什么？确定杂草和传染病的有效控制程序已成为一个重大的全球环境问题。在世界各地，本地植物群落正在被非本地植物取代，地方性野生动物疾病正在对人类构成威胁。特别是农业用地和牧地，其原生植物群落结构已发生改变，特别容易受到外来植物入侵。生活在疾病动物宿主附近的人类感染该疾病的风险增加。本研究的目标是将本项目开发的数学模型和理论技术应用于两个重要而及时的生物学问题：(1)农田或牧场杂草的控制；(2)野生动物种群狂犬病的控制。数学模型的制定、分析和数值模拟为控制田地或牧场杂草蔓延和野生动物狂犬病的有效方法提供了更好的理解。对各种控制策略进行比较，以确定最有效的短期和长期策略，以防止或减少传播，同时对环境造成最小的损害或变化，并对人类造成最小的风险。

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.