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Abstract In this work we present a C-MATH-NN framework that extends a C-MATH framework that was developed in recent years to include prediction using artificial neural networks (NN) in a way that is engaging, interdisciplinary and collaborative to help equip our next generation of students with advanced technological and critical thinking skills motivated by social good. Specifically, the C-MATH framework has successfully helped students understand a real-worldContextthrough a mathematicalModelwhich is thenAnalyzedmathematically andTestedthrough appropriate numerical methods with data, and finally this undergraduate research becomes aHabitfor students. Furthermore, the explanation of the main components of a simple NN-model serves as an introduction to this popular artificial intelligence tool. This framework has contributed to the success of talented students in mathematical biology research and their academic goals. We present a visual introduction to the architecture of artificial neural networks and its application to disease dynamics for all interested learners. We introduce a simple feed forward physics-informed neural network (PINN) built in MS-Excel that works very well for an epidemiological model and an equivalent Python implementation that is robust and scalable. The products introduced in this work are shared in an online repository with curriculum material for students and instructors that includes MS-Excel workbooks and Python files to facilitate the acquisition of technology tools to explore and use in their own projects. 

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. 

Graph convolutional neural networks (GCNs) have shown tremendous promise in addressing data-intensive challenges in recent years. In particular, some attempts have been made to improve predictions of Susceptible-Infected-Recovered (SIR) models by incorporating human mobility between metapopulations and using graph approaches to estimate corresponding hyperparameters. Recently, researchers have found that a hybrid GCN-SIR approach outperformed existing methodologies when used on the data collected on a precinct level in Japan. In our work, we extend this approach to data collected from the continental US, adjusting for the differing mobility patterns and varying policy responses. We also develop the strategy for real-time continuous estimation of the reproduction number and study the accuracy of model predictions for the overall population as well as individual states. Strengths and limitations of the GCN-SIR approach are discussed as a potential candidate for modeling disease dynamics. 

Since the discovery of COVID-19 in Wuhan, China in 2019, close to seven million people have died from the infection. At the onset of the pandemic, many countries enacted stringent measures such as school and event closings in a bid to control and curtail the spread of the virus, leading to many within-household infections as people spent more time at home. This study develops an agent-based model (ABM) to gain insight into the impact of government COVID-19 mitigation guidelines and policy options on within-household and community COVID-19 infections in Gauteng, South Africa. Gauteng is the province in South Africa having the smallest land area, but it accounts for 25.8% of the country’s population. Agents are randomly assigned to cells on a $1000\times 1000$square grid varying according to Gauteng’s population density and household size distribution. We found that the percentage of within-household infections is higher in communities with smaller population densities, with the reverse being true for communities with larger population densities. Furthermore, as the agents’ movement activation rate increases, community-related infections increase, especially in communities with small population densities. Our study found an interesting phenomenon, observed for the first time: the existence of a movement activation threshold where the percentage and number of outside household infections overtake the percentage and number of within household infections when the activation rate increases. Lastly, our simulation results captured the two epidemic peaks experienced in Gauteng from March 30, 2020 to June 22, 2021 while varying quarantine violation and movement activation rates. Thus, the developed ABM can be used to exploit the implications of COVID-19 mitigation guidelines and policy options on household transmission to provide interesting insights. 

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.