Reopening Borders in the Early Stage of COVID-19 Massive Vaccination: A Mathematic Model to Estimate the Optimal Length of Quarantine Period between Different Regions

Background: Quarantine for cross-region traveling has slowed the transmission of SARS-CoV-2/coronavirus. However, it has had a negative impact on mental health and economic recovery. The study aimed to estimate a responsible and pragmatic quarantine period using a mathematic model.  Method: We constructed a retrospective mathematical modeling using data from the World Health Organization coronavirus disease database. Four risk levels and 16 different cross-border scenarios were designed and analyzed. We then sought the optimal quarantine duration in different situations using a logarithmic regression analysis.  Findings: The mean optimal quarantine days was found to be 1·4, 6·5, 10, and 14 days for the scenarios of traveling from very-high-risk countries to very-high-, high-, moderate- and low-risk countries, respectively. The mean optimal quarantine days regarding from high-risk countries to very-high-, high-, moderate- and low-risk countries were 0, 0·8, 7·2, and 14 days, respectively. The mean optimal quarantine days for from moderate-risk countries to very-high-, high-, moderate-, and low-risk countries were 0, 0·8, 2·6, and 10·4 days, respectively. The mean optimal quarantine days for from low-risk countries to very high-, high-, moderate-, and low-risk countries were 0, 0, 0, and 2 days, respectively. Correlations in logarithmic regression between the optimal quarantine days and the ratio of incidence rate between different countries performed well. Interpretation: The quarantine period for cross-region travelling could be adjusted based on the ratio of incidence rate between the two countries. We recommend a optimal quarantine period for travelers from a low-risk country entering a higher risk country in the early stage of COVID-19 massive vaccination.  Funding: No external funding Declaration of Interest: None to declare