Incorporating Immunity into Epidemiological Infectious Disease Models: Bridging Multiple Scales

新出现的和正在发生的传染病爆发严重影响人口的健康和经济稳定。由于个体的差异，特别是个体对各种感染的保护水平不同，理解和预测此类疫情的进程具有挑战性。这项工作将涉及全世界关注的三种传染病：登革热、疟疾和百日咳。简单的数学模型已经成功地描述了简单传染病的流行，并提出了针对简单传染病的干预策略。然而，更复杂的疾病需要开发和分析更复杂的模型，特别是连接多个尺度-生物体，时间和空间。新的模型和定量工具将有助于深入了解观察到的暴发模式的原因，并指导防治这些复杂疾病的战略。这项工作将为本科生和研究生提供跨学科培训，工作成果将通过开展以传染病为基础的外联活动和同行评议的出版物和研讨会传播给广泛的受众。了解人群中可变免疫的作用对于准确确定流行病的动态以及有效减缓和阻止其传播至关重要。这项工作包括开发、分析和模拟具有个体宿主免疫反应可变性的多尺度模型。详细的宿主免疫动态将被纳入登革热、疟疾和百日咳的人口水平流行病学模型，以评估人口水平的疾病动态。这项工作的目的有三个方面：确定宿主内病毒和免疫变异对登革热流行病学动态的作用；确定适应性抗原特异性免疫对疟疾流行和传播潜力的作用；并建立一个免疫减弱和增强的模型，以确定百日咳的最佳初级疫苗接种和加强剂量。这项工作通过在种群模型中纳入宿主内异质性，进一步推动了多尺度微分方程系统的数学理论。它将建立在微分方程和非线性动力系统的数学理论基础上。主要的挑战将是分析具有可变时间尺度和大维度的非线性系统。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。

Emerging and on-going infectious disease outbreaks significantly impact the health and economic stability of a population. Understanding and predicting the course of such outbreaks is challenging due to the variability of individuals, particularly with respect to their levels of protection against various infections. This work will address three infectious diseases of worldwide interest: dengue, malaria and whooping cough. Simple mathematical models have been successful at describing the epidemics of and suggesting intervention strategies for simple infectious disease. More complicated diseases, however, require the development and analysis of more complicated models, particularly linking multiple scales - organismal, temporal, and spatial. The novel models and quantitative tools will provide insight into the reason for observed patterns of outbreaks as well as guide strategies for combating these complicated diseases. This work will provide interdisciplinary training for undergraduate and graduate students, and the results of the work will be disseminated to a broad audience through the development of infectious disease based outreach activities and peer-reviewed publications and seminars.Understanding the role of variable immunity within populations is crucial to accurately determining the dynamics of epidemics and to effectively slowing and stopping their spread. This work includes the development, analysis, and simulation of multi-scale models with variability of the individual host immune response. Detailed within-host immune dynamics will be incorporated into population-level epidemiological models of dengue, malaria and pertussis (whooping cough) to evaluate population-level disease dynamics. The aims of this work are three fold: determine the role of within-host viral and immune variability on epidemiological dynamics of dengue; determine the role of adaptive antigen-specific immunity on malaria prevalence and transmission potential; and develop a model of waning and boosting of immunity to determine optimal primary vaccination and booster dose timing for pertussis. This work furthers the mathematical theory of multi-scale systems of differential equations motivated through the incorporation of within-host heterogeneity in population models. It will build upon mathematical theory from differential equations and non-linear dynamical systems. The main challenge will be analyses of non-linear systems with variable time scales and large dimensionality.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.