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

该项目涉及一类新的数学模型，该模型通过人们感染疾病的总天数来量化疾病爆发。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公共卫生政策，疾病干预措施和疾病演变的评估。作为概念验证，该项目将对麻疹、百日咳和流感等历史疾病爆发进行建模，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。研究结果将有助于公共卫生官员作出明智的决定所需的信息和疾病演变的知识状态。该项目将开发和应用一类新的微分方程分区模型。这类模型是第一个考虑另一种假设，即如何量化人口中的疾病数量。通过考虑“感染人日”与“疾病发生率”的数量，新一类模型能够将潜伏期和感染期分布的更高统计矩纳入控制模型动态的速率中。这项工作的目的是说明这一类新的房室模型及其应用的直接，准确，易于解释的属性。该项目将分析以下问题：1）健康差异和毒力演变之间的相互作用，2）传染期离群值对疾病干预措施成本效益的影响，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。该研究将说明这类新模型的实用性，有助于公共卫生官员所需的信息，以减轻疾病爆发，并有助于对疾病演变的知识状态。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

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.