RUI: Applications of a Generalized Differential Equation Compartmental Model of Infectious Disease Transmission

这个项目涉及一类新的数学模型，它通过人们感染某种疾病的总天数来量化疾病的爆发。该项目的目标是应用这些模型来回答公共卫生和进化生物学中的开放性问题。这些模型可以提供一种简单的方法来研究人们从感染中恢复时间的差异如何影响对公共卫生政策、疾病干预和疾病演变的评估。作为概念验证，该项目将模拟历史上的疾病暴发，如麻疹、百日咳和流感，并将预测结果与基于跟踪感染人数的经典建模方法进行比较。预计研究结果将有助于提供公共卫生官员作出知情决定所需的信息，并有助于了解疾病演变的知识状况。本项目将开发和应用一类新的微分方程单元模型。这类模型首先考虑了另一种假设，即如何量化人群中的疾病数量。通过考虑“人日感染”的数量超过“疾病发病率”，新一类模型能够将来自潜伏期和传染期分布的较高统计时刻合并到控制模型动力学的比率中。这项工作的目的是说明直截了当的，准确的，并且易于解释的性质，这类新的隔室模型及其应用。该项目将分析以下问题：1)健康差异与毒力进化之间的相互作用，2)感染期异常值对疾病干预成本效益的影响，以及3)宿主变异如何影响传染病传播的进化和流行病学动态。解决这些问题的关键将是使用平均剩余寿命理论和分析技术，包括稳定性、成本效益和进化入侵分析。这项研究将说明这类新模型的效用，有助于公共卫生官员减轻疾病爆发所需的信息，并有助于了解疾病演变的状况。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This project concerns a novel class of mathematical models that quantify disease outbreaks by the total number of days people are infected with a disease. The goal of the project is to apply these models to answer open questions in public health and evolutionary biology. The models can provide a simple means to study how the differences in peoples’ recovery time from infection affects the evaluation of public health policies, disease interventions, and disease evolution. As proof of concept, the project will model historical disease outbreaks, such as measles, whooping cough, and influenza, and compare predictions to classical modeling approaches that are based on tracking the number of infected people. The results of the research are expected to contribute to both the information needed by public health officials to make informed decisions and the state of knowledge on disease evolution.This project will develop and apply a new class of differential equation compartmental models. This class of models is the first to consider an alternative assumption as to what quantifies the amount of disease in a population. By considering the quantity "person-days of infection" over "disease incidence," the new class of models enables the incorporation of higher statistical moments from latent and infectious period distributions into the rates that govern the dynamics of the model. The work aims to illustrate the straightforward, accurate, and readily interpretable properties of this new class of compartmental model and its application. The project will analyze questions such as 1) the interplay between health disparities and virulence evolution, 2) the impact of infectious period outliers on the cost-effectiveness of disease interventions, and 3) how host variation affects the evolutionary and epidemiology dynamics of infectious disease transmission. Essential in tackling these issues will be the use of mean-residual life theory and analysis techniques that include stability, cost-effectiveness, and evolutionary invasion analyses. The research will illustrate the utility of this new class of models, contribute to the information needed by public health officials to mitigate disease outbreaks, and contribute to the state of knowledge on disease evolution.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.