[Paper Review] A simplified model for expected development of the SARS-CoV-2 (Corona) spread in Germany and US after social distancing

Françoise Schmitt|arXiv (Cornell University)|Mar 24, 2020

COVID-19 epidemiological studies6 references15 citations

TL;DR

This study proposes a simplified epidemiological model to assess the impact of social distancing on SARS-CoV-2 transmission in Germany and the US. By analyzing daily infection growth rates, it demonstrates that reducing the daily growth rate from 30–35% to 10% would drastically slow the pandemic, suggesting that timely and strict social distancing measures can effectively control viral spread.

ABSTRACT

Widespread opinions and discussion exist regarding the efficiency of social distancing after crucial spread of the SARS-CoV-2 virus during the actual Covid-19 pandemic. While Germany has released a federal law that prohibits any type of direct contact for more than 2 people other countries including the US released curfews. People are now wondering whether these measures are helpful to stop or hamper the Covid-19 pandemic and to limit the spread of the new corona virus. A quantitative statement on this question depends on many parameters that are difficult to grasp mathematically and cannot therefore be made conclusively (they include consistent adherence to the measures decided, the estimated number of unreported cases, the possible limitation by test capacities, possible mutations of the virus, etc ...). However, it turns out that a reduction in the actual daily new infection rate (actual daily growth rate of reported cases, in short: infection rate) from the current value of 30-35% in the US to 10% would be extremely effective in stopping the spread of the virus. The severe restrictions in Germany which closed any public events, schools and universities a week ago might already have contributed to a reduction of the growth rate of reported cases below 30%.

Motivation & Objective

• To evaluate the effectiveness of social distancing measures in reducing SARS-CoV-2 transmission in Germany and the US.
• To quantify the impact of different daily infection growth rates on pandemic progression.
• To assess whether current social distancing policies are sufficient to curb the spread of the virus.
• To provide a simple, interpretable model for policymakers to evaluate intervention outcomes without complex modeling.
• To estimate the threshold growth rate below which the pandemic would begin to slow significantly.

Proposed method

• The model uses reported case data to track the daily growth rate of confirmed infections in Germany and the US.
• It compares the actual daily growth rate before and after implementation of social distancing measures.
• The analysis focuses on changes in the infection rate, defined as the percentage increase in new cases per day.
• The model assumes that a reduction in the daily growth rate to 10% would significantly slow transmission.
• It evaluates the impact of policy changes such as school closures and event bans on the observed growth rate.
• The model does not include detailed compartmental dynamics (e.g., SIR), but relies on observed trends in reported case growth.

Experimental results

Research questions

• RQ1 To what extent does social distancing reduce the daily growth rate of SARS-CoV-2 cases in Germany and the US?
• RQ2 What level of daily infection growth rate is required to achieve effective control of the pandemic?
• RQ3 How effective are strict measures like school closures and event bans in reducing transmission?
• RQ4 Can a simplified model based on observed case growth rates reliably predict the impact of social distancing?
• RQ5 What is the threshold growth rate below which the pandemic would begin to decline?

Key findings

• The daily infection growth rate in the US was observed to be between 30% and 35% at the time of the study.
• In Germany, the implementation of strict social distancing measures—including closure of schools and public events—appears to have reduced the daily growth rate of reported cases below 30%.
• A reduction in the daily growth rate from 30–35% to 10% would be extremely effective in slowing the spread of SARS-CoV-2.
• The model suggests that such a reduction could lead to a significant decline in new infections over time.
• The study highlights that the effectiveness of social distancing depends critically on reducing the daily growth rate to a low level.
• The results indicate that timely and stringent interventions can meaningfully alter the course of the pandemic.