Avian Flu: Modeling, Analysis, and Simulations

相对温和的人类流感病毒株常年感染我们中的许多人，尽管频率是季节性的，但有时可能演变为一种潜在的致命病毒株，能够引发大流行。1918年、1957年和1968年的三次人类流感大流行--分别被称为“西班牙流感”、“亚洲流感”和“香港流感”--造成了巨大的破坏，无论是人命损失还是随之而来的经济影响。对于其中的每一种，遗传证据表明，一种新的流感病毒株是由动物流感病毒株和人类流感病毒株在共同感染这两种病毒的共同宿主物种内的基因重组(“转移”)进化而来的。这种新进化的毒株对人类产生了灾难性的影响，因为宿主对这种毒株缺乏自然免疫力。最近在世界多个地区发生的禽流感病毒感染和死亡病例，以及人类和其他动物(如猪)可以作为禽流感和人类流感病毒株的共同宿主的事实，引发了人们的担忧，即我们可能在短期内出现另一种新型和高毒力的病毒株，从而可能发生另一场大流行。数学模型为理解、可能预测和控制新的病原体菌株的出现和随后的传播提供了至关重要的工具。在这个项目中，我们开发和分析了数学和模拟模型来研究真实世界的生物场景，在这个场景中，人类宿主被禽流感和人类流感毒株共同感染。我们将特别集中于表征新出现的毒力菌株在人类群体中入侵和持续的条件。这个项目将极大地提高我们对禽流感从禽类传播到人类种群以及一般多物种流行病系统的传播动力学和进化的了解。它将提供一系列基于现有数据的可用的、现实的模型。这些模型可以作为未来扩展的坚实背景，纳入和测试各种大流行流感控制措施(如疫苗接种、化疗和社会距离)的有效性，并提出了对疾病预测特别重要的实证研究途径。在技术方法方面，该项目联合数学家和生物学家的努力，基于集成偏微分方程(PDE)、常微分方程(ODE)和随机个体模拟(IBS)建立模型，以研究禽流感(AI)的进化流行病学和种群生物学。研究目标将沿着两个主要方向进行。1)流感病毒基因组进化的“漂移”和“转移”机制将被同时纳入一个多毒株PDE模型，然后将被用于预测一种进化的流感变异在人类群体中的流行病学后果--一种具有高致病性和高人传播率的新型禽流感病毒株。该模型的ODE版本将与世界卫生组织(世卫组织)现有的人类感染禽流感累计病例数数据相适应。然后将对最佳拟合的常微分方程组和偏微分方程模型进行数学分析，以严格描述传播和持续的条件。2)基于个体的互补模拟(IBS)模型将在小世界类型的网络上建立，该网络包含每个个体的显式社会交互(接触)邻域以及出生、死亡和感染事件的随机过程。这些IBS模型中的流感暴发模式将从基础网络结构和与相应ODE模型的预测相关的角度进行研究。这将有助于阐明在菌株出现的早期阶段可能很重要的随机因素的作用。

The relatively benign human influenza virus strain that infects many of us year-round, albeit with seasonal pulses in frequency, can sometimes evolve into a potentially deadly strain that is capable of triggering a pandemic. The three recent human flu pandemics of 1918, 1957 and 1968--respectively known as the "Spanish flu", "Asian flu", and "Hong Kong flu"--caused huge devastation both in terms of the loss of human lives and consequent economic impacts. For each of these, genetic evidence suggests that a novel influenza strain evolved from the genetic recombination ("shift") of an animal flu strain and a human flu strain within a common host species that was co-infected by these two strains. This newly evolved strain had catastrophic effects on humans because of the absence of natural immunity by the host to this strain. The recent cases of human infection and death from avian influenza virus in several parts of the world, and the fact that humans and other animal species (such as swine) can act as a shared host to both avian flu and human flu strains, has raised concern that we may face a near-term emergence of another novel and highly virulent strain, thus another potential pandemic. Mathematical models provide crucial tools for understanding and possibly predicting and controlling the emergence and subsequent spread of novel pathogen strains. In this project we develop and analyze mathematical and simulation models to study real-world biological scenarios, in which there is co-infection of human host by avian flu and human flu strains. We will focus in particular on characterizing conditions for invasion and persistence of emergent virulent strains within human populations. This project will significantly advance our knowledge of the transmission dynamics and evolution of avian influenza from bird to human populations in particular, and of multi-species epidemic systems in general. It will provide a series of usable, realistic models that are grounded on available data. These models can serve as a solid background for future extensions incorporating and testing the efficacy of various control measures (such as vaccination, chemotherapy, and social distancing) for pandemic influenza, and suggest avenues of empirical study that are particularly important to pursue for disease prediction.In terms of technical approaches, this project unites the efforts of mathematicians and biologists in developing models based on integrated partial differential equations (PDE), ordinary differential equations (ODE), and stochastic individual-based simulations (IBS), to study the evolutionary epidemiology and population biology of avian influenza (AI). The research goal will be pursued along two main directions. 1) The "drift" and "shift" mechanisms of genomic evolution of an influenza virus will be simultaneously incorporated within a multi-strain PDE model that then will be used to predict the epidemiological consequences in a human population of an evolved influenza variant -- a novel avian influenza strain with both high pathogenicity and high human-to-human transmission efficiency. ODE versions of this model will be fitted to available World Health Organization (WHO) data of the cumulative number of human cases of avian influenza infection. Mathematical analysis of the best fitting ODE and PDE models will then be carried out, to rigorously characterize conditions for spread and persistence. 2) Complementary individual-based simulation (IBS) models of a human population will be developed on a small-world type network that incorporate explicit social interaction (contact) neighborhoods of each individual, and stochastic processes of birth, death and infection events. The pattern of flu outbreaks in these IBS models will be studied with respect to the underlying network structure, and related to the predictions of the corresponding ODE models. This will help elucidate the role of stochastic factors likely to be important in the early stages of strain emergence.