Control Strategies for COVID-19 Epidemic with Vaccination, Shield Immunity and Quarantine: A Metric Temporal Logic Approach

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

A framework for simultaneous task allocation and planning under uncertainty

We present novel techniques for simultaneous task allocation and planning in multi-robot systems operating under uncertainty. By performing task allocation and planning simultaneously, allocations are informed by individual robot behaviour, creating more efficient team behaviour. We go beyond existing work by planning for task reallocation across the team given a model of partial task satisfaction under potential robot failures and uncertain action outcomes. We model the problem using Markov decision processes, with tasks encoded in co-safe linear temporal logic, and optimise for the expected number of tasks completed by the team. To avoid the inherent complexity of joint models, we propose an alternative model that simultaneously considers task allocation and planning, but in a sequential fashion. We then build a joint policy from the sequential policy obtained from our model, thus allowing for concurrent policy execution. Furthermore, to enable adaptation in the case of robot failures, we consider replanning from failure states and propose an approach to preemptively replan in an anytime fashion, replanning for more probable failure states first. Our method also allows us to quantify the performance of the team by providing an analysis of properties such as the expected number of completed tasks under concurrent policy execution. We implement and extensively evaluate our approach on a range of scenarios. We compare its performance to a state-of-the-art baseline in decoupled task allocation and planning: sequential single-item auctions. Our approach outperforms the baseline in terms of computation time and the number of times replanning is required on robot failure