A Framework for Inferring Epidemiological Model Parameters using Bayesian Nonparametrics

Abstract

The use of epidemiological models for decision-making has been prominent during the COVID-19 pandemic. Our work presents the application of nonparametric Bayesian techniques for inferring epidemiological model parameters based on available data sets published during the pandemic, towards enabling predictions under uncertainty during emerging pandemics. We present a methodology and framework that allows epidemiological model drivers to be integrated as input into the model calibration process. We demonstrate our methodology using the stringency index and mobility data for COVID-19 on an SEIRD compartmental model for selected US states. Our results directly compare the use of Bayesian nonparametrics for model predictions based on best parameter estimates with results of inference of parameter values across the US states. The proposed methodology provides a framework for What-If analysis and sequential decision-making methods for disease intervention planning and is demonstrated for COVID-19, while also applicable to other infectious disease models.

Figure 1:

Calibrated SEIRD model output of the total confirmed cases as well as the learned β and $R_0=\frac{\beta }{\gamma }$ values.

Figure 2:

Plots of the mean and covariance (including the parameter samples) learned from GP regression for the State of New York. Figure 2a illustrates the relationship between stringency values and calibrated transmission rates (β). Figure 2b illustrates relationship between observed mobility and β. Figure 2c illustrates the relationship between both stringency and observed mobility with β. The mean value of β represented in the pixel value in the range [0, 1].

Figure 3:

SEIRD model predictions of the total confirmed cases.