LEAPS-MPS: Incorporating Stratification by Vaccination Status and Virus Variants in Mathematical Models of Infectious Disease Spread

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。自2019冠状病毒病大流行开始以来，数学建模在评估和预测疾病影响以及指导公共卫生政策方面发挥了重要作用。然而，现有的数学框架在适应疾病传播动态的突然变化方面进展缓慢，这是由疫苗免疫力下降和新冠病毒变体（如丁型病毒和组粒病毒）的出现造成的。该项目将通过开发数据驱动的数学建模工具来应对这些挑战，这些工具根据具有不同特征的因素（例如由于疫苗接种状况和病毒变体传播的差异造成的因素）对人群进行划分。随着COVID-19的发展并在全球人口中成为流行病，制定的框架将指导公共卫生官员评估潜在疫苗接种策略的有效性，并评估变异改变疾病传播过程的能力。这将促进有针对性和有影响力的政策，而不是破坏性的全民限制和封锁。该项目将让本科生参与主题应用数学研究，并支持STEM中代表性不足的学生，特别关注底特律地铁的非裔美国人社区。该项目将进一步推动劳伦斯理工大学的课程和项目发展，这将增强该机构的研究环境，并进一步实现首席研究员在劳伦斯理工大学建立一个持续的、以学生为中心的跨学科数学生物学研究项目的专业目标。传染病传播的传统数学建模框架往往忽略了群体内异质传播的因素。这可能导致对流行病学参数（如基本繁殖数和群体免疫阈值）的错误估计，对疾病传播机制的错误评估以及不准确的预测。该项目将发展与常微分方程系统相关的隔间sir型（易感-感染-恢复）模型的理论和应用，以纳入人口疫苗接种覆盖率的差异、不同的免疫减弱期以及具有不同流行病学特征的病毒变体之间的竞争。免疫减弱将通过接种疫苗或以前感染后恢复易感性的γ分布延迟纳入。本文将利用线性链技巧对得到的分布延迟微分方程进行分析和数值模拟，该技巧将伽马分布延迟降低为指数延迟的线性链。来自密歇根州卫生与公众服务部的病例数据将用于参数化和验证模型，目的是在不同的免疫接种计划下为COVID-19的传播提供有见地的预测。通过将感染类别划分为具有变异特异性参数的不同区室，如传播性、严重程度、疫苗耐药性、再感染率和诊断检测方面的差异，将病毒变异纳入其中。目标将是建立新的临界阈值，以确定病毒变体何时可以在人群中持续存在或成为优势，并解决从早期生长阶段估计变体的流行病学参数的相反问题。通过控制人口的疫苗接种覆盖水平，开发的模型将能够突破病例发病率数据的复杂性，为推动疾病传播的主要因素提供关键见解。将开发能够执行这些模型并与公共卫生数据库连接的用户友好的计算包。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 award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).Since the beginning of the COVID-19 pandemic, mathematical modeling has played a significant role in assessing and forecasting the impacts of the disease and guiding public health policy. Existing mathematical frameworks, however, have been slow to adapt to sudden changes in disease spread dynamics resulting from the waning vaccine immunity and emergence of COVID-19 variants such as delta and omicron. This project will address these challenges by developing data-driven mathematical modeling tools which divide populations according to factors that have distinct characteristics, such as those due to differences in vaccination status and the spread of virus variants. As COVID-19 evolves and becomes endemic in the global population, the developed frameworks will guide public health officials in evaluating the effectiveness of potential vaccination strategies and assessing the capacity of variants to alter the course of disease spread. This will facilitate targeted and impactful policies rather than disruptive population-wide restrictions and lockdowns. The project will engage undergraduate students in topical applied mathematics research and support underrepresented students in STEM with a particular focus on the African American community in Metro Detroit. The project will additionally advance curricular and program development at Lawrence Technological University, which will enhance the institution's research environment and further the principal investigator’s professional goal of establishing a sustained, student-focused, and interdisciplinary research program in mathematical biology at Lawrence Technological University.Traditional mathematical modeling frameworks of infectious disease spread often ignore factors of heterogeneous spread within a population. This can lead to poor estimates of epidemiological parameters (such as the basic reproduction number and herd immunity threshold), mistaken assessments of the mechanisms of disease spread, and inaccurate forecasts. This project will develop the theory and application of compartmental SIR-type (Susceptible-Infectious-Recovered) models, which are associated with a system of ordinary differential equations, to incorporate variances in a population's vaccination coverage level, differing waning immunity periods, and competition between virus variants with distinct epidemiological characteristics. Waning immunity will be incorporated through a gamma-distributed delay on return to susceptibility after vaccination or previous infection. The resulting distributed delay differential equations will be analyzed and numerically simulated using the linear chain trick, which reduces gamma-distributed delays to a linear chain of exponential delays. Case data from The Michigan Department of Health and Human Services will be used to parametrize and validate the models with the goal of providing insightful forecasts for the spread of COVID-19 under different immunization schedules. Virus variants will be incorporated by dividing the infectious class into distinct compartments with variant-specific parameters, such as variances in transmissibility, severity, vaccine resistance, reinfection rate, and diagnostic detection. The goal will be to establish novel critical thresholds for when a virus variant can persist or become dominant in a population as well as address the inverse question of estimating a variant's epidemiological parameters from its early-stage growth. By controlling a population's vaccination coverage level, the developed models will be able to cut through the complexity of case incidence data to provide critical insights into the primary factors driving disease spread. User-friendly computational packages capable of implementing the models and interfacing with public health databases will be developed.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.