Forecasting the spread of COVID-19 under different reopening strategies

The COVID-19 pandemic has caused widespread disruption globally, impacting lives and economies significantly. While much research focuses on the disease's impact and treatments, understanding how prevention measures, such as social distancing, affect the spread of COVID-19 is crucial. The standard SIR model, commonly used to study disease spread, assumes a linear relationship between the number of infectious individuals and the rate of new infections. This paper challenges that assumption, arguing that the interconnected nature of social networks leads to a non-linear relationship. The research aims to develop a modified SIR model that incorporates this non-linearity, providing more accurate forecasts of COVID-19 spread under different reopening strategies and levels of social distancing.

Existing literature predominantly employs the SIR model and its variants (e.g., SEIR) to study COVID-19 spread. These models have been applied to various geographical regions and have yielded insights into the impact of lockdowns and travel restrictions. However, these studies often assume a linear relationship between the number of infectious individuals and the infection rate. This paper acknowledges the existing work but argues that the standard SIR model's limitations stem from its inability to account for the complex social network structures that influence disease transmission.

This study uses a modified SIR model to account for the non-linear relationship between the number of infectious individuals and the rate of new infections. The model incorporates several key features: 1. **Concave Relationship:** The model introduces an exponent (ω) on the number of infectious individuals, allowing for a concave relationship where the marginal impact of each additional infectious individual diminishes as the number of infected individuals increases. This is in contrast to the standard SIR model where ω = 1. 2. **Transmission Rate:** The transmission rate (Rit) is modeled as a function of several factors including social distancing (dit), temperature (mit), and humidity (hit). This allows for the examination of the influence of various factors on the spread of COVID-19. 3. **Data Sources:** County-level data on COVID-19 cases, social distancing (derived from SafeGraph cellphone GPS data), temperature, and humidity are used. The authors acknowledge that the number of officially diagnosed cases likely underestimates the true number of infections and use an approximation to adjust for this. 4. **Estimation:** The model is estimated using a logarithmic transformation and an instrumental variable (IV) approach to address potential endogeneity bias arising from the correlation between social distancing and the error term. Rainfall is used as an instrument for social distancing. 5. **Forecasting:** Out-of-sample forecasts are generated using a hold-out sample of 75 days (May 24 – August 6) and simulated under different social distancing scenarios (25%, current, 75%, and 100% return-to-normalcy) from August 7 to October 31, 2020.

The estimated model yields several key findings: 1. **Concave Spread:** The estimated value of ω (0.57) confirms the concave relationship between the number of infectious individuals and new infections. This implies that the initial exponential growth of COVID-19 quickly stabilizes into a prolonged plateau. 2. **Impact of Social Distancing:** Social distancing is found to have a substantial negative impact on the growth rate of COVID-19. 3. **Other Factors:** Humidity shows a smaller positive effect on transmission rates, while temperature is insignificant. 4. **Demographic Factors:** Analysis of county fixed effects reveals that population density, the percentage of commuters using public transport, and the fraction of Black and Hispanic residents are associated with higher contagion rates. Seniors also exhibit higher contagion rates compared to other age groups. 5. **Out-of-Sample Prediction:** The modified SIR model (ω = 0.57) outperforms the standard SIR model (ω = 1) in out-of-sample predictions for both the US nationally and specifically in Florida, Georgia, and Wisconsin. 6. **Simulation Results:** Simulations under different reopening levels show that a return to pre-COVID social distancing levels would lead to a substantial surge in cases, although these would eventually plateau. Maintaining stricter social distancing would significantly curb the spread. The model consistently shows an almost linear growth pattern in cumulative cases after reopening.

The findings address the research question by demonstrating the importance of accounting for the non-linearity of COVID-19 spread due to the interconnected nature of social networks. The modified SIR model provides more accurate forecasts than the standard SIR model, highlighting the limitations of linear assumptions. The significant impact of social distancing underscores the effectiveness of non-pharmaceutical interventions. The results have significant implications for policymakers in designing reopening strategies and public health interventions. Future research could explore the model's robustness under different assumptions and data sources, investigate the role of other factors influencing transmission, and further refine the model to enhance predictive accuracy.

This paper presents a modified SIR model that accurately captures the non-linear spread of COVID-19, emphasizing the significance of interconnected social networks. The model's superior out-of-sample predictive power and simulations highlight the substantial impact of social distancing on the trajectory of the pandemic. The findings offer crucial insights for policymakers to implement evidence-based strategies for reopening and mitigating future outbreaks. Future research could focus on incorporating additional factors like testing capacity, vaccination rates, and variants of the virus into the model.

The study's limitations include the reliance on officially reported cases, which might underestimate the true infection numbers. The instrumental variable approach, while mitigating endogeneity bias, depends on the validity of the rainfall instrument. The model's generalizability to other regions and future pandemics requires further investigation.