Monitoring and Forecasting COVID-19: Heuristic Regression, Susceptible-Infected-Removed Model and, Spatial Stochastic.

P.L De Andres,L Hoessly,L De Andres-Bragado

doi:10.3389/fams.2021.650716

Abstract

The COVID-19 pandemic has had worldwide devastating effects on human lives, highlighting the need for tools to predict its development. The dynamics of such public-health threats can often be efficiently analyzed through simple models that help to make quantitative timely policy decisions. We benchmark a minimal version of a Susceptible-Infected-Removed model for infectious diseases (SIR) coupled with a simple least-squares Statistical Heuristic Regression (SHR) based on a lognormal distribution. We derive the three free parameters for both models in several cases and test them against the amount of data needed to bring accuracy in predictions. The SHR model is ≈ ±2% accurate about 20 days past the second inflexion point in the daily curve of cases, while the SIR model reaches a similar accuracy a fortnight before. All the analyzed cases assert the utility of SHR and SIR approximants as a valuable tool to forecast the disease’s evolution. Finally, we have studied simulated stochastic individual-based SIR dynamics, which yields a detailed spatial and temporal view of the disease that cannot be given by SIR or SHR methods.

Highlights

The consequences of a pandemic like COVID-19 caused by the virus SARS-CoV-2 cannot be overstated (Nature, 2021)
This study aims to take advantage of available worldwide data on COVID-19 (Roser et al, 2021; Dong et al, 2020) to benchmark and assign error bars to minimal models, like the susceptibleinfected-recovered (SIR) with different sophistication levels (Kermack and McKendrick, 1927; Weiss, 2013; He et al, 2020a; Yang and Wang, 2020; Khan et al, 2020; Annas et al, 2020), a straightforward least-squares best-fit (LS) Statistical Heuristic Regression based on a lognormal distribution (Lam, 1988), or basic Monte-Carlo simulation (Girona, 2020; Gang, 2020)
We have proved that a least-squares Statistical Heuristic Regression (SHR)-model based on the lognormal distribution is well suited to describe the epidemic’s evolution using only two free parameters per infection wave

Summary

Introduction

The consequences of a pandemic like COVID-19 caused by the virus SARS-CoV-2 cannot be overstated (Nature, 2021). Frontiers in Applied Mathematics and Statistics | www.frontiersin.org de Andres et al. Monitoring and Forecasting COVID-19 requires, at worst, a brute force search in p-dimensional parameter space. There are no general polynomial bounds on the time complexity given in the number of samples and the search space dimension. These models are gauged against two variables measured daily: 1) the number of deaths, and 2) the number of new infections. We show that the simultaneous monitoring of both observables supplemented with relatively simple mathematical approaches can be used to follow and forecast the evolution of the disease with enough accuracy to help decision-making processes and we discuss the associated error bars

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Conclusion