Collaborative Research: DMS/NIGMS 1: Identifiability investigation of Multi-scale Models of Infectious Diseases

病原体的出现和重新出现及其对社会的影响加强了以下必要性： 在科学领域和生物尺度上的整合和协同作用，以增进了解， 预测和应对病原体的传播多尺度数学模型，考虑时间 在对人群传播进行建模时， 最佳干预措施的建议。使用多尺度评估数据时的一个缺点 模型来自于感染和传播的扩展阶段的数据稀缺， 在每个尺度上的数据量和频率，以及所考虑的模型的复杂性。到 为了确定参数估计中组合偏差的来源，我们将使用一种组合的理论-实验方法来研究多尺度模型的结构和实际参数可辨识性 传染性疾病的研究，可以为最佳的实验设计提供信息。拟议的研究将促进 更好地了解多尺度模型拟合多尺度传染病时的不确定性来源 疾病数据，重点是非洲猪瘟和SARS-CoV-2病毒。通过结合经验和理论 我们的目标是确定多尺度模型的结构和实际参数的可识别性， 为最佳实验设计提供信息，并提高我们做出预测和建议的能力。 干预措施。我们的建议将集中在三个主要的数学挑战：（1）发展方法， 提高宿主内系统的实际可识别性;（2）使用实验数据为开发 （3）建立多尺度参数可辨识性预测的定量框架 系统.本文的总体目标是建立多尺度的数学模型， 开发和统计模型，用于与纵向病毒滴度和概率收集数据拟合 为了减少不确定性和提高结果的再现性，这将最终 提高我们对传染病传播和持久性的认识。

The emergence and re-emergence of pathogens and their impact on society has reinforced the need for integration and synergy across scientific fields and biological scales in order to advance understanding, predicting, and responding to pathogen spread. Multi-scale mathematical models that consider the timing and length of individual infections when modeling transmission into the population can aid recommendations for optimal interventions. One shortcoming when evaluating data using multi-scale models comes from data scarcity in the expansion stages of the infection and transmission, the differences in data magnitude and frequency at each scale, together with the complexity of the models considered. To determine the source of combined biases in parameter estimation, we will use a combined empirical-theoretical approach for investigating structural and practical parameter identifiability of multi-scale models of infectious diseases that may inform optimal experimental design. The proposed research will facilitate a better understanding of the sources of uncertainty when fitting multi-scale models to multi-scale infectious disease data, with a focus on Usutu and SARS-CoV-2 viruses. By combining empirical and theoretical approaches we aim to determine structural and practical parameter identifiability of multi-scale models, to inform optimal experimental design, and to improve our ability to make predictions and suggest interventions. Our proposal will focus on three major mathematical challenges: (1) Developing methods for improving practical identifiability in within-host systems; (2) Use experimental data to inform development of transmission models; (3) Build a quantitative framework to predict parameter identifiability in multi-scale systems. The overarching goal of the proposed work is to integrate multi-scale mathematical model development and statistical models for data fitting with collection of longitudinal virus titers and probability of transmission data in order to decrease uncertainty and improve results reproducibility. This will ultimately improve our understanding of infection disease transmission and persistence.