Dynamics and Evolution of Emerging Diseases with Applications to Amphibians

该项目的目标有三个：(1)为宿主-病原体系统进化的数学理论做出贡献；(2)将该理论应用于两栖动物种群；(3)对南部高平原两栖动物种群及其相关疾病进行深入的生物学调查。具有宿主和病原体遗传学的确定性和随机结构化流行病模型将被开发、分析和数值模拟。离散和连续时间结构模型是基于差分方程，微分方程，马尔可夫链和随机微分方程。这些数学模型将用于研究疾病如何影响持久性、持续时间、流行病的发生和种群大小，以及宿主和病原体如何共同进化以应对各种控制策略和不同的选择压力。这些模型将应用于南部高平原的特定两栖动物种群。拟进行的研究包括为期三年的实验调查（两年密集的实地调查），以确定南部高平原两种常见两栖动物——虎蝾螈和平原掌足蟾蜍的数量、疾病流行率和免疫学特征。研究地点包括南部高平原上的12个湖。本研究收集的数据的数学和统计分析解决了一些基本的生物学问题，如两栖动物丰度、免疫反应、疾病流行、生命周期阶段（幼虫、幼兽和成虫）、土地利用方式（草地与农田）和气候条件之间的关系。这项研究为确定在两栖动物疾病传播和持续中具有重要意义的关键因素提供了重要信息。人类和野生动物传染病的出现是对公共卫生和全球生物多样性保护的重大威胁。人口密度增加、农业和畜牧业的变化、水坝建设、森林砍伐、对野生动物栖息地的侵占、气候变化、环境污染以及病原体进入新地区是导致传染病出现的一些因素。了解导致这些疾病出现的病原体的动态，以及它们的宿主和环境之间复杂和不断变化的关系，对于这些疾病的潜在控制是必要的。各种各样的人类和环境影响导致许多宿主-病原体系统进化并适应这些变化的影响，使控制成为一项更加困难的任务。迫切需要理论研究来帮助我们理解宿主-病原体系统的进化。本研究的目的是建立、分析和模拟基于流行病学、遗传学和种群动力学原理的数学模型，并将这些模型应用于宿主-病原体系统，并对特定的宿主-病原体系统进行实验研究。在拟议的调查中开发的宿主种群模型专门适用于两栖动物种群。全球两栖动物数量的减少被认为是当今最紧迫和最神秘的环境问题之一。最近的证据表明，新出现的疾病（病毒和真菌病原体）是青蛙、蟾蜍和蝾螈大规模死亡的原因。事实上，最近在两栖动物中爆发的疾病应该得到认真关注，因为它们可能标志着全球范围内的环境变化，可能威胁到许多生物。拟议研究的主要部分包括两年的实地调查和三年的实验室调查。摘要本研究旨在探讨南方高平原两种常见两栖动物的数量、疾病流行及免疫学特征。该研究为今后两栖动物种群数量下降的原因研究奠定了基础。这项资助是在DMS/NIGMS联合倡议下提供的，以支持数学生物学领域的研究资助。这是一个由美国国家科学基金会数学科学部（DMS）和美国国立卫生研究院国家综合医学科学研究所（NIGMS）联合主办的竞赛。

The goals of this project are threefold: (1) to contribute to the mathematical theory of the evolution of host-pathogen systems, (2) to apply the theory to amphibian populations, and (3) to conduct an intensive biological investigation of amphibian populations and their associated diseases on the Southern High Plains. Deterministic and stochastic structured epidemic models with host and pathogen genetics will be developed, analyzed, and numerically simulated. Discrete and continuous time structured models are based on difference equations, differential equations, Markov chains, and stochastic differential equations. The mathematical models will be used to study how disease affects persistence, duration, onset of an epidemic, and population size, and how host and pathogen coevolve in response to various control strategies and to different selection pressures. The models will be applied to specific amphibian populations on the Southern High Plains. The proposed research includes a three-year experimental investigation (two years of intensive fieldwork) to determine amphibian abundance, disease prevalence, and immunological characteristics of two common species of amphibians on the Southern High Plains, the tiger salamander and the plains spadefoot toad. The study sites consist of twelve playa lakes on the Southern High Plains. Mathematical and statistical analyses of the data collected from this study address some basic biological questions about the relationships among amphibian abundance, immune response, disease prevalence, life cycle stage (larvae, juvenile, and adult), landuse practices (grassland versus cropland), and climatic conditions. This study provides important information for determining critical factors that are significant in the transmission and persistence of diseases in amphibians. The emergence of infectious diseases in humans and wildlife is a major threat to public health and to the conservation of global biodiversity. Increased population densities, changes in agricultural and livestock practices, dam building, deforestation, encroachment into wildlife habitat, climate change, environmental pollution, and introduction of pathogens into new areas are some of the factors leading to the emergence of infectious diseases. Understanding the dynamics of the pathogens responsible for the emergence of these diseases and the complex and changing relationship between their host and their environment is needed for potential control of these diseases. A variety of human and environmental influences have caused many host-pathogen systems to evolve and to adapt to these changing influences, making control an even more difficult task. Theoretical studies which contribute to our understanding of the evolution of host-pathogen systems are urgently needed. It is the purpose of this investigation to develop, analyze, and simulate mathematical models based on principles from epidemiology, genetics and population dynamics, to apply these models to host-pathogen systems, and to conduct an experimental investigation on a particular host-pathogen system. The host population models developed in the proposed investigation are applied specifically to amphibian populations. The global decline in amphibian populations is thought to be one of the most pressing and enigmatic environmental problems today. Recent evidence indicates that emerging diseases (viral and fungal pathogens) are responsible for mass die-offs of frogs, toads, and salamanders. Indeed, recent outbreaks of diseases in amphibians should be given serious attention as they may signal environmental change on a global scale that may threaten many organisms. A major part of the proposed research involves a two-year field and three-year laboratory investigation. The purpose of the experimental investigation is to assess amphibian abundance, disease prevalence, and immunological characteristics of two common species of amphibians on the Southern High Plains. This study lays the groundwork for future studies on causes of population declines in amphibians. This grant is made under the Joint DMS/NIGMS Initiative to Support Research Grants in the Area of Mathematical Biology. This is a joint competition sponsored by the Division of Mathematical Sciences (DMS) at the National Science Foundation and the National Institute of General Medical Sciences (NIGMS) at the National Institutes of Health.