2 research outputs found
Control of Generalized Discrete-time SIS Epidemics via Submodular Function Minimization
In this paper, we study a novel control method for a generalized SIS epidemic
process. In particular, we use predictive control to design optimal protective
resource distribution strategies which balance the need to eliminate the
epidemic quickly against the need to limit the rate at which protective
resources are used. We expect that such a controller may be useful in
mitigating the spread of biological diseases which do not confer immunity to
those who have been infected previously, with sexually transmitted infections
being a prominent example of such. Technically, this paper provides a novel
contribution in demonstrating that the particular combinatorial optimal control
problem used to design resource allocations has an objective function which is
submodular, and so can be solved in polynomial time despite its combinatorial
nature. We test the performance of the proposed controller with numerical
simulations, and provide some comments on directions for future work.Comment: 6 pages; 3 figure
Robust Economic Model Predictive Control of Continuous-time Epidemic Processes
In this paper, we develop a robust economic model predictive controller for
the containment of stochastic Susceptible-Exposed-Infected-Vigilant (SEIV)
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.Comment: 16 pages, 3 figures; Revision to correct minor typos and clarify some
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