Spatial and temporal dynamics of SARS-CoV-2: Modeling, analysis and simulation.

A reaction-diffusion viral infection model is formulated to characterize the infection process of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a heterogeneous environment. In the model, the viral production, infection and death rates of compartments are given by the general functions. We consider the well-posedness of the solution, derive the basic reproduction number R 0 , discuss the global stability of uninfected steady state and explore the uniform persistence for the model. We further propose a spatial diffusion SARS-CoV-2 infection model with humoral immunity and spatial independent coefficients, and analyze the global attractivity of uninfected, humoral inactivated and humoral activated equilibria which are determined by two dynamical thresholds. Numerical simulations are performed to illustrate our theoretical results which reveal that diffusion, spatial heterogeneity and incidence types have evident impact on the SARS-CoV-2 infection process which should not be neglected for experiments and clinical treatments.

An epidemic-economic model for COVID-19.

In this paper, we propose a new mathematical model to study the epidemic and economic consequences of COVID-19, with a focus on the interaction between the disease transmission, the pandemic management, and the economic growth. We consider both the symptomatic and asymptomatic infections and incorporate the effectiveness of disease control into the respective transmission rates. Meanwhile, the progression of the pandemic and the evolution of the susceptible, infectious and recovered population groups directly impact the mitigation and economic development levels. We fit this model to the reported COVID-19 cases and unemployment rates in the US state of Tennessee, as a demonstration of a real-world application of the modeling framework.

From Policy to Prediction: Forecasting COVID-19 Dynamics Under Imperfect Vaccination.

Understanding the joint impact of vaccination and non-pharmaceutical interventions on COVID-19 development is important for making public health decisions that control the pandemic. Recently, we created a method in forecasting the daily number of confirmed cases of infectious diseases by combining a mechanistic ordinary differential equation (ODE) model for infectious classes and a generalized boosting machine learning model (GBM) for predicting how public health policies and mobility data affect the transmission rate in the ODE model (Wang et al. in Bull Math Biol 84:57, 2022). In this paper, we extend the method to the post-vaccination period, accordingly obtain a retrospective forecast of COVID-19 daily confirmed cases in the US, and identify the relative influence of the policies used as the predictor variables. In particular, our ODE model contains both partially and fully vaccinated compartments and accounts for the breakthrough cases, that is, vaccinated individuals can still get infected. Our results indicate that the inclusion of data on non-pharmaceutical interventions can significantly improve the accuracy of the predictions. With the use of policy data, the model predicts the number of daily infected cases up to 35 days in the future, with an average mean absolute percentage error of [Formula: see text], which is further improved to [Formula: see text] if combined with human mobility data. Moreover, the most influential predictor variables are the policies of restrictions on gatherings, testing and school closing. The modeling approach used in this work can help policymakers design control measures as variant strains threaten public health in the future.

A Hypothesis-Free Bridging of Disease Dynamics and Non-pharmaceutical Policies.

Accurate prediction of the number of daily or weekly confirmed cases of COVID-19 is critical to the control of the pandemic. Existing mechanistic models nicely capture the disease dynamics. However, to forecast the future, they require the transmission rate to be known, limiting their prediction power. Typically, a hypothesis is made on the form of the transmission rate with respect to time. Yet the real form is too complex to be mechanistically modeled due to the unknown dynamics of many influential factors. We tackle this problem by using a hypothesis-free machine-learning algorithm to estimate the transmission rate from data on non-pharmaceutical policies, and in turn forecast the confirmed cases using a mechanistic disease model. More specifically, we build a hybrid model consisting of a mechanistic ordinary differential equation (ODE) model and a gradient boosting model (GBM). To calibrate the parameters, we develop an "inverse method" that obtains the transmission rate inversely from the other variables in the ODE model and then feed it into the GBM to connect with the policy data. The resulting model forecasted the number of daily confirmed cases up to 35 days in the future in the USA with an averaged mean absolute percentage error of 27%. It can identify the most informative predictive variables, which can be helpful in designing improved forecasters as well as informing policymakers.