Control strategies for COVID-19 epidemic with vaccination, shield immunity and quarantine: A metric temporal logic approach

Abstract

Ever since the outbreak of the COVID-19 epidemic, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. We study three specific COVID-19 epidemic control models: the susceptible, exposed, infectious, recovered (SEIR) model with vaccination control; the SEIR model with shield immunity control; and the susceptible, un-quarantined infected, quarantined infected, confirmed infected (SUQC) model with quarantine control. We express the control requirement in metric temporal logic (MTL) formulas (a type of formal specification languages) which can specify the expected control outcomes such as “the deaths from the infection should never exceed one thousand per day within the next three months” or “the population immune from the disease should eventually exceed 200 thousand within the next 100 to 120 days”. We then develop methods for synthesizing control strategies with MTL specifications. To the best of our knowledge, this is the first paper to systematically synthesize control strategies based on the COVID-19 epidemic models with formal specifications. We provide simulation results in three different case studies: vaccination control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; shield immunity control for the COVID-19 epidemic with model parameters estimated from data in Lombardy, Italy; and quarantine control for the COVID-19 epidemic with model parameters estimated from data in Wuhan, China. The results show that the proposed synthesis approach can generate control inputs such that the time-varying numbers of individuals in each category (e.g., infectious, immune) satisfy the MTL specifications. The results also show that early intervention is essential in mitigating the spread of COVID-19, and more control effort is needed for more stringent MTL specifications. For example, based on the model in Lombardy, Italy, achieving less than 100 deaths per day and 10000 total deaths within 100 days requires 441.7% more vaccination control effort than achieving less than 1000 deaths per day and 50000 total deaths within 100 days.

A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up

“…In the early stages of the pandemic in the UK, Crellen et al (2021) used an SEIR model to investigate the e↵ect of di↵erent mean durations of immunity (90-365 days), on short-term dynamics and long-term endemic behaviour, in an age-based model, in the absence of vaccination, under various assumptions about the time-varying e↵ective reproduction number. In Xu, Wu, and Topcu (2021), the authors consider a short-term SEIR model over 200 days, that optimises vaccination roll-out, subject to thresholds on death rates, cumulative deaths, and target numbers of those vaccinated. It assumes 100% vaccine e cacy, with no waning of immunity following vaccination or infection.…”

“…Models developed by Xu, Wu, and Topcu (2021), Ghostine et al (2021), Wintachai andPrathom (2021), andAntonini, Calandrini, andBianconi (2021) are age-homogeneous. In the early stages of the pandemic in the UK, Crellen et al (2021) used an SEIR model to investigate the e↵ect of di↵erent mean durations of immunity (90-365 days), on short-term dynamics and long-term endemic behaviour, in an age-based model, in the absence of vaccination, under various assumptions about the time-varying e↵ective reproduction number.…”

Measuring the impact of COVID-19 vaccination and immunity waning: a modelling study for Portugal

“…These vaccines have shown promising effects and mass vaccination programmes are underway worldwide. While such programmes are promising, several modelling studies have shown that as vaccination is rolled out, proper vaccine allocation is necessary [5,6,7,8,9] and maintenance of NPIs is still required to prevent the increase of hospitalisations and deaths, particularly before completing full vaccination [10,11,12,13,14]. In Portugal, vaccination has been rolled out in two main phases: the first focused in healthcare professionals and vulnerable individuals (residents in nursing homes, individuals at higher risk of severe disease due to preexisting medical conditions and those aged ≥ 80 years old), and the second one for the general population, organised by age groups, from 79 years old downwards.…”

Which features of an outpatient treatment for COVID-19 would be most important for pandemic control? A modelling study

“…[ 16 ] or Xu et al . [ 17 ], vaccination is modelled in a new compartment of SIR-type by considering that susceptible individuals are vaccinated without delay.…”

“…Concerning pharmaceutical interventions, most of the models deal with the vaccination. In Dashtbali & Mirzaie [14], Giordano et al [15], Moore et al [16] or Xu et al [17], vaccination is modelled in a new compartment of SIR-type by considering that susceptible individuals are vaccinated without delay.…”