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2022 European Control Conference, ECC 2022 ; : 743-748, 2022.
Article in English | Scopus | ID: covidwho-2013200

ABSTRACT

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that in the MRPI all restrictions can be lifted without violating the infection cap, we choose a suitable subset of the MRPI to define terminal constraints in our MPC routine and show that the number of infected people decays exponentially within this set. Furthermore, under mild assumptions we prove existence of a uniform bound on the time required to reach this terminal region (without violating the infection cap) starting in the admissible set. The findings are substantiated based on a numerical case study. © 2022 EUCA.

2.
Siam Journal on Control and Optimization ; 60(2):S145-S169, 2022.
Article in English | English Web of Science | ID: covidwho-1883309

ABSTRACT

In this paper, we provide insights on how much testing and social distancing is re-quired to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: incubation time, age-dependent symptom severity, and testing and hospital-ization delays;the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd im-munity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.

3.
Siam Journal on Applied Dynamical Systems ; 20(2):1135-1157, 2021.
Article in English | Web of Science | ID: covidwho-1354592

ABSTRACT

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision-making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the health care system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.

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