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

杂草和传染病传播和控制模型的开发和分析

• 批准号: 9626417
• 负责人: Linda Allen
• 金额: $ 8.85万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-15 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626417&HistoricalAwards=false
• 关键词: Development; Analysis; Models; Spread; Control

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.

艾伦9626417这项研究的目标涉及两个不同但相关的生物领域。一个区域是杂草控制，另一个区域是控制传染病。 就其本质而言，杂草和传染病药物是宿主系统中不必要的入侵者。 他们的介绍经常会产生不利影响。 控制杂草和传染病的实用方法正在持续的研究和发展下。 但是，这些控制程序需要理论上的理由和可预测性。 该项目开发和分析数学模型，这些模型为评估这些控制程序提供了定量和定性的手段。 集成差方程为建模这两个过程的生物学动力学提供了一个现实的起点。时间变量是离散的，但是空间和状态变量是连续的。 离散的时间模型描述了植物种群，其世代是不重叠的和流行病的，其中观察病例或动物的季节性运动和人口密度与离散时间间隔有关。 分析了杂草和传染病的数学模型，以确定空间分散，年龄或阶段结构，多人群相互作用以及一般生长假设对模型行为的影响。 解决了两个重要的问题：（i）杂草或疾病散布的速度？ （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。 在世界范围内，本地植物群落被非本地植物流离失所，而恩津野生动植物疾病正成为对人类的威胁。 特别是，已经改变了本地植物群落结构的农业土地和牧场特别容易受到引入的植物物种的入侵。 靠近疾病的动物水库的人类患疾病的风险增加。 这项研究的目的是将该项目中开发的数学模型和理论技术应用于两个重要且及时的生物学问题：（1）控制农田或牧场中的杂草，以及（2）控制野生动植物种群中的狂犬病。 数学模型的制定，分析和数值模拟为控制杂草在田间或牧场和野生动植物中狂犬病中杂草传播的有效方法提供了更大的理解。 比较各种控制策略，以确定最有效的短期和长期策略，以防止或减少差异，同时造成最小的损害或改变环境，并对人类的风险最小。