Bayesian-based predictions of COVID-19 evolution in Texas using multispecies mixture-theoretic continuum models

Abstract

We consider a mixture-theoretic continuum model of the spread of COVID-19 in Texas. The model consists of multiple coupled partial differential reaction-diffusion equations governing the evolution of susceptible, exposed, infectious, recovered, and deceased fractions of the total population in a given region. We consider the problem of model calibration, validation, and prediction following a Bayesian learning approach implemented in OPAL (the Occam Plausibility Algorithm). Our goal is to incorporate COVID-19 data to calibrate the model in real-time and make meaningful predictions and specify the confidence level in the prediction by quantifying the uncertainty in key quantities of interests. Our results show smaller mortality rates in Texas than what is reported in the literature. We predict 7003 deceased cases by September 1, 2020 in Texas with 95% CI 6802-7204. The model is validated for the total deceased cases, however, is found to be invalid for the total infected cases. We discuss possible improvements of the model. Keywords Bayesian statistics • Model inference • Disease dynamics • Mixture theory • COVID-19 • SARS-CoV-2 virus 1 Introduction Modeling the spreading of infectious diseases can help in extracting relevant information from the data, such as effective reproduction rates, mortality rates, contact rates, in exploring the effectiveness of various preventive measures and their effect on the epidemic, developing a deeper understanding of how the particular disease spreads and major features that support the spreading, [15]. During 2020, much of the world has been under lockdown due to a novel SARS-CoV-2 virus. The virus originated in Wuhan, China, and has resulted in the loss of many lives, loss of livelihood, and almost complete shutdown of economies. SARS-CoV-2 virus infection spreads via droplets generated during coughing/sneezing and touching contaminated surfaces. To slow down its spread, people are advised to maintain social dis

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Adaptive mesh refinement and coarsening for diffusion–reaction epidemiological models

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