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The COVID-19 pandemic is a global threat presenting health, economic, and social challenges that continue to escalate. Metapopulation epidemic modeling studies in the susceptible–exposed–infectious–removed (SEIR) style have played important roles in informing public health policy making to mitigate the spread of COVID-19. These models typically rely on a key assumption on the homogeneity of the population. This assumption certainly cannot be expected to hold true in real situations; various geographic, socioeconomic, and cultural environments affect the behaviors that drive the spread of COVID-19 in different communities. What’s more, variation of intracounty environments creates spatial heterogeneity of transmission in different regions. To address this issue, we develop a human mobility flow-augmented stochastic SEIR-style epidemic modeling framework with the ability to distinguish different regions and their corresponding behaviors. This modeling framework is then combined with data assimilation and machine learning techniques to reconstruct the historical growth trajectories of COVID-19 confirmed cases in two counties in Wisconsin. The associations between the spread of COVID-19 and business foot traffic, race and ethnicity, and age structure are then investigated. The results reveal that, in a college town (Dane County), the most important heterogeneity is age structure, while, in a large city area (Milwaukee County), racial and ethnic heterogeneity becomes more apparent. Scenario studies further indicate a strong response of the spread rate to various reopening policies, which suggests that policy makers may need to take these heterogeneities into account very carefully when designing policies for mitigating the ongoing spread of COVID-19 and reopening. 

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Quantifying the model error and model uncertainty plays an important role in understanding and predicting complex dynamical systems. In the first part of this article, a simple information criterion is developed to assess the model error in imperfect models. This effective information criterion takes into account the information in both the equilibrium statistics and the temporal autocorrelation function, where the latter is written in the form of the spectrum density that permits the quantification via information theory. This information criterion facilitates the study of model reduction, stochastic parameterizations, and intermittent events. In the second part of this article, a new efficient method is developed to improve the computation of the linear response via the Fluctuation Dissipation Theorem (FDT). This new approach makes use of a Gaussian Mixture (GM) to describe the unperturbed probability density function in high dimensions and avoids utilizing Gaussian approximations in computing the statistical response, as is widely used in the quasi-Gaussian (qG) FDT. Testing examples show that this GM FDT outperforms qG FDT in various strong non-Gaussian regimes.