Abstract
The management of COVID-19 appears to be a long-term challenge, even in countries that have managed to suppress the epidemic after their initial outbreak. In this paper, we propose a model predictive approach for the constrained control of a nonlinear compartmental model that captures the key dynamical properties of COVID-19. The control design uses the discrete-time version of the epidemic model, and it is able to handle complex, possibly time-dependent constraints, logical relations between model variables and multiple predefined discrete levels of interventions. A state observer is also constructed for the computation of non-measured variables from the number of hospitalized patients. Five control scenarios with different cost functions and constraints are studied through numerical simulations, including an output feedback configuration with uncertain parameters. It is visible from the results that, depending on the cost function associated with different policy aims, the obtained controls correspond to mitigation and suppression strategies, and the constructed control inputs are similar to real-life government responses. The results also clearly show the key importance of early intervention, the continuous tracking of the susceptible population and that of future work in determining the true costs of restrictive control measures and their quantitative effects.
Highlights
On December 31, 2019, China alerted the World Health Organization (WHO) on a cluster of pneumonia cases of unknown origin in Wuhan, China
The aim of this paper is to propose an optimization-based control approach for compartmental epidemic models constructed for the COVID-19 outbreak, which is able to take into account complex, possibly time-dependent specifications including bounds, and even logical relations between model variables, and multiple predefined discrete levels of interventions
The control input, denoted by u, reflects the effect of the measures implemented to reduce the transmission rate. This variable is introduced in the model as a scaling factor of β, i.e., β is replaced by β(1 − u) in Eqs. (1) and (2) which are modified to Nonlinear model predictive control with logic constraints
Summary
On December 31, 2019, China alerted the World Health Organization (WHO) on a cluster of pneumonia cases of unknown origin in Wuhan, China. The aim of this paper is to propose an optimization-based control approach for compartmental epidemic models constructed for the COVID-19 outbreak, which is able to take into account complex, possibly time-dependent specifications including bounds, and even logical relations between model variables, and multiple predefined discrete levels of interventions. Another important goal is to study the possibilities of output feedback design by applying a dynamic state observer. We parameterize our model to Hungary, but it can be generalized to other countries as well
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have