individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results are also consistent with the claim that control in the early phases of COVID-19 is the most effective in the mitigation.'
author:
- 'Zhe Xu[^1],  Bo Wu and Ufuk Topcu'
bibliography:
- 'ref.bib'
title: 'Control Strategies for COVID-19 Epidemic with Vaccination, Shield Immunity and Quarantine: A Metric Temporal Logic Approach'
---

Introduction
============

The COVID-19 pandemic [@Fauci2020] has caused over 15 million confirmed cases and over 0.6 million deaths globally as of July 23, 2020. Ever since the outbreak of COVID-19, various public health control strategies have been produced and tested against SARS-CoV-2 [@Stewart_magazine_2020].

Currently, over 90 vaccines are being developed against SARS-CoV-2 by research teams across the world [@vaccines_nature2020]. Besides vaccination, other strategies have also been proposed to control the spread of SARS-CoV-2. In [@Weitz_nature], the authors proposed *shielding immunity* to protect the susceptible people from getting infected with SARS-CoV-2. Specifically, shielding immunity works by first identifying and deploying recovered individuals who have protective antibodies to SARS-CoV-2, and then increasing the proportion of interactions with recovered individuals as opposed to other individuals. In [@Zhao2020], the authors analyzed how quarantine has mitigated the spread of SARS-CoV-2 based 