Robust Economic Model Predictive Control of Continuous-Time Epidemic Processes

Abstract

In this paper, we develop a robust economic model predictive controller for the containment of stochastic Susceptible-Exposed-Infected-Vigilant pSEIV q epidemic processes which drives the process to extinction quickly, while minimizing the rate at which control resources are used. The work we present here is significant in that it addresses the problem of efficiently controlling general stochastic epidemic systems without relying on mean-field approximation, which is an important issue in the theory of stochastic epidemic processes. This enables us to provide rigorous convergence guarantees on the stochastic epidemic model itself, improving over the mean-field type convergence results of most prior work. There are two primary technical difficulties addressed in treating this problem: (i) constructing a means of tractably approximating the evolution of the process, so that the designed approximation is robust to the modeling error introduced by the applied moment closure, and (ii) guaranteeing that the designed controller causes the closed-loop system to drive the SEIV process to extinction quickly. As an application, we use the developed framework for optimizing the use of quarantines in containing an SEIV epidemic outbreak.

Epidemics control model with consideration of seven-segment population model

“…As a result, there is a risk that the optimal policy ends up chocking the medical support system. Similarly, the other approaches such as [3,15] do not consider hospitalization and treatment as part of the model and hence the decisions are not well informed. Since the proposed model incorporates the information of the individuals under treatment, the individuals in quarantine, the exposed individuals, and the associated transition probabilities, the resulting optimal policy successfully avoids large peaks in the number of individuals under treatment or quarantine at any given time.…”

“…Many control techniques have been developed for control in epidemiology [1,2]. For example, predictive (or model predictive control based) techniques [3,4], stochastic techniques [5,6], Markov chain based techniques [7,8], Markov decision processes (MDP) based techniques [9][10][11], optimal control (mostly Pontryagin's maximum principle) based techniques [2,12], and recently, network-based techniques [13][14][15]. This paper proposes an MDP based model.…”

“…However, we have sketched a possible solution in Sect. 3. Also, once a problem is formulated as an MDP, it is entitled to many approximate dynamic programming algorithms [16][17][18] for calculation of a quasi-optimal control policy with reduced computational complexity.…”

A hybrid model integrating warm heat and ultraviolet germicidal irradiation might efficiently disinfect respirators and personal protective equipment

“…Considering the model of WUVH as a single input and single-output system, we effectively use an approach where the outputs can be forecasted. Model predictive control 32 , 33 is used to forecast the system behavior. This is a feedback model and is used to predict the current values depending upon the difference between the actual and predicted values.x…”

Control of Generalized Discrete-Time SIS Epidemics via Submodular Function Minimization

“…It was shown in [10] that for any priority order strategy, there exists a sufficiently large budget so as to guarantee that the epidemic is driven out of the network quickly. It was shown in [11] that it is possible to construct a system of ordinary differential equations which gives provable upper-and lower-bounds on infection statistics, and to use these approximations to N enforce a stability constraint that guarantees fast extinction of the epidemic. However, in all of these works, the optimization problems which fundamentally characterize the controllers are N P-hard.…”