A Statistical and Dynamical Model for Forecasting COVID-19 Deaths based on a Hybrid Asymmetric Gaussian and SEIR Construct
Authors: Syage Jack A. 
Published: June 2020

Background

The limitations of forecasting (real-time statistical) and predictive (dynamic epidemiological) models have become apparent as COVID-19 has progressed from a rapid exponential ascent to a slower decent, which is dependent on unknowable parameters such as extent of social distancing and easing. We present a means to optimize a forecasting model by functionalizing our previously reported Asymmetric Gaussian model with SEIR-like parameters. Conversely, SEIR models can be adapted to better incorporate real-time data.

Methods

Our previously reported asymmetric Gaussian model was shown to greatly improve on forecasting accuracy relative to use of symmetric functions, such as Gaussian and error functions for death rates and cumulative deaths, respectively. However, the reported asymmetric Gaussian implementation, which fitted well to the ascent and much of the recovery side of the real death rate data, was not agile enough to respond to changing social behavior that is resulting in persistence of infections and deaths in the later stage of recovery. We have introduced a time-dependent σ(t) parameter to account for transmission rate variability due to the effects of behavioral changes such as social distancing and subsequent social easing. The σ(t) parameter is analogous to the basic reproduction number R0 (infection factor) that is evidently not a constant during the progression of COVID-19 for a particular population. The popularly used SEIR model and its many variants are also incorporating a time dependent R0(t) to better describe the effects of social distancing and social easing to improve predictive capability when extrapolating from real-time data.

Results

Comparisons are given for the previously reported Asymmetric Gaussian model and to the revised, what we call, SEIR Gaussian model. We also have developed an analogous model based on R0(t) that we call SEIR Statistical model to show the correspondence that can be attained. It is shown that these two models can replicate each other and therefore provide similar forecasts based on fitting to the same real-time data. We show the results for reported U.S. death rates up to June 12, 2020 at which time the cumulative death count was 113,820. The forecasted cumulative deaths for these two models and compared to the University of Washington (UW) IHME model are 140,440, 139,272, and 149,690 (for 8/4/20) and 147,819, 148, 912, and 201,129 (for 10/1/20), respectively. We also show how the SEIR asymmetric Gaussian model can also account for various scenarios of social distancing, social easing, and even re-bound outbreaks where the death and case rates begin climbing again.

Conclusions

Forecasting models, based on real-time data, are essential for guiding policy and human behavior to minimize the deadly impact of COVID-19 while balancing the need to socialize and energize the economy. It is becoming clear that changing social behavior from isolation to easing requires models that can adapt to the changing transmission rate in order to more accurately forecast death and case rates. We believe our asymmetric Gaussian approach has advantages over modified SEIR models in offering simpler governing equations that are dependent on fewer variables.