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Abstract More than half of the coronavirus disease 19 (COVID-19) related mortality rates in the United States and Europe are associated with long-term-care facilities (LTCFs) such as old-age organizations, nursing homes, and disability centers. These facilities are considered most vulnerable to spread of an pandemic like COVID-19 because of multiple reasons including high density of elderly population with a diverse range of medical requirements, limited resources, nursing activities/medications, and the role of external visitors. In this study, we aim to understand the role of visitor’s family members and specific interventions (such as use of face masks and restriction of visiting hours) on the dynamics of infection in a community using a mathematical model. The model considers two types of social contexts (community and LTCFs) with three different groups of interacting populations (non-mobile community individuals, mobile community individuals, and long-term facility residents). The goal of this work is to compare the outbreak burden between different centre of disease control (CDC) planning scenarios, which capture distinct types of intensity of diseases spread in LTCF observed during COVID-19 outbreak. The movement of community mobile members is captured via their average relative times in and out of the long-term facilities to understand the strategies that would work well in these facilities the CDC planning scenarios. Our results suggest that heterogeneous mixing worsens epidemic scenario as compared to homogeneous mixing and the epidemic burden is hundreds times greater for community spread than within the facility population. 

In late 2019, the emergence of COVID-19 in Wuhan, China, led to the implementation of stringent measures forming the zero-COVID policy aimed at eliminating transmission. Zero-COVID policy basically aimed at completely eliminating the transmission of COVID-19. However, the relaxation of this policy in late 2022 reportedly resulted in a rapid surge of COVID-19 cases. The aim of this work is to investigate the factors contributing to this outbreak using a new SEIR-type epidemic model with time-dependent level of immunity. Our model incorporates a time-dependent level of immunity considering vaccine doses administered and time-post-vaccination dependent vaccine efficacy. We find that vaccine efficacy plays a significant role in determining the outbreak size and maximum number of daily infected. Additionally, our model considers under-reporting in daily cases and deaths, revealing their combined effects on the outbreak magnitude. We also introduce a novel Physics Informed Neural Networks (PINNs) approach which is extremely useful in estimating critical parameters and helps in evaluating the predictive capability of our model. 

The emergence of COVID-19 in the United States resulted in a series of federal and state-level lock-downs and COVID-19 related health mandates to manage the spread of the virus. These policies may negatively impact the mental health state of the population. This study focused on the trends in mental health indicators following the COVID-19 pandemic amongst four United States geographical regions, and political party preferences. Indicators of interest included feeling anxious, feeling depressed, and worried about finances. Survey data from the Delphi Group at Carnegie Mellon University were analyzed using clustering algorithms and dynamic connectome obtained from sliding window analysis. Connectome refers to the description of connectivity on a network. United States maps were generated to observe spatial trends and identify communities with similar mental health and COVID-19 trends. Between March 3rd, 2021, and January 10th, 2022, states in the southern geographic region showed similar trends for reported values of feeling anxious and worried about finances. There were no identifiable communities resembling geographical regions or political party preference for the feeling depressed indicator. We observed a high degree of correlation among southern states as well as within Republican states, where the highest correlation values from the dynamic connectome for feeling anxious and feeling depressed variables seemingly overlapped with an increase in COVID-19 related cases, deaths, hospitalizations, and rapid spread of the COVID-19 Delta variant. 

In the past few years, approaches such as physics informed neural networks (PINNs) have been applied to a variety of applications that can be modeled by linear and nonlinear ordinary and partial differential equations. Specifically, this work builds on the application of PINNs to a SIRD (susceptible, infectious, recovered, and dead) compartmental model and enhances it to build new mathematicalmodels that incorporate transportation between populations and their impact on the dynamics of infectious diseases. Our work employs neural networks capable of learning how diseases spread, forecasting their progression, and finding their unique parameters. We show how these approaches are capable of predicting the behavior of a disease described by governing differential equations that include parameters and variables associated with the movement of the population between neighboring cities. We show that our model validates real data and also how such PINNs based methodspredict optimal parameters for given datasets. 

Accurate numerical and physical models play an important role in modeling the spread of infectious disease as well as informing policy decisions. Vaccination programs rely on the estimation of disease parameters from limited, error-prone reported data. Using physics-informed neural networks (PINNs) as universal function approximators of the susceptible-infected-recovered (SIR) compartmentalized differential equation model, we create a data-driven framework that uses reported data to estimate disease spread and approximate corresponding disease parameters. We apply this to datafrom a London boarding school, demonstrating the framework's ability to produce accurate disease and parameter estimations despite noisy data. However, real-world populations contain sub-populations, each exhibiting different levels of risk and activity. Thus, we expand our framework to model meta-populations of preferentially-mixed subgroups with various contact rates, introducing a new substitution to decrease the number of parameters. Optimal parameters are estimated throughPINNs which are then used in a negative gradient approach to calculate an optimal vaccine distribution plan for informed policy decisions. We also manipulate a new hyperparameter in the loss function of the PINNs network to expedite training. Together, our work creates a data-driven tool for future infectious disease vaccination efforts in heterogeneously mixed populations.