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

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.