Adaptive Susceptible-Infectious-Removed Model for Continuous Estimation of the COVID-19 Infection Rate and Reproduction Number in the United States: Modeling Study

Abstract

Background: The dynamics of the COVID-19 pandemic vary owing to local population density and policy measures. During decision-making, policymakers consider an estimate of the effective reproduction number R_t, which is the expected number of secondary infections spread by a single infected individual.

Objective: We propose a simple method for estimating the time-varying infection rate and the R_t.

Methods: We used a sliding window approach with a Susceptible-Infectious-Removed (SIR) model. We estimated the infection rate from the reported cases over a 7-day window to obtain a continuous estimation of R_t. A proposed adaptive SIR (aSIR) model was applied to analyze the data at the state and county levels.

Results: The aSIR model showed an excellent fit for the number of reported COVID-19 cases, and the 1-day forecast mean absolute prediction error was <2.6% across all states. However, the 7-day forecast mean absolute prediction error approached 16.2% and strongly overestimated the number of cases when the R_t was rapidly decreasing. The maximal R_t displayed a wide range of 2.0 to 4.5 across all states, with the highest values for New York (4.4) and Michigan (4.5). We found that the aSIR model can rapidly adapt to an increase in the number of tests and an associated increase in the reported cases of infection. Our results also suggest that intensive testing may be an effective method of reducing R_t.

Conclusions: The aSIR model provides a simple and accurate computational tool for continuous R_t estimation and evaluation of the efficacy of mitigation measures.

Keywords: COVID-19; SARS-CoV-2; United States; compartmental models; decision-making; estimate; infection rate; infectious disease; modeling; pandemic; prediction; reproduction number.