arXiv subjects

Denis Nikitin

Publications and source records attributed to Denis Nikitin.

3 recordsLinked to original sources

arXiv2021

Effective Testing Policies for Controlling an Epidemic Outbreak

Testing is a crucial control mechanism for an epidemic outbreak because it enables the health authority to detect and isolate the infected cases, thereby limiting the disease transmission to susceptible people, when no effective treatment or vaccine is available. In this paper, an epidemic model that incorporates the testing rate as a control input is presented. The proposed model distinguishes between the undetected infected and the detected infected cases with the latter assumed to be isolated from the disease spreading process in the population. Two testing policies, effective during the onset of an epidemic when no treatment or vaccine is available, are devised: (i) best-effort strategy for testing (BEST) and (ii) constant optimal strategy for testing (COST). The BEST is a suppression policy that provides a lower bound on the testing rate to stop the growth of the epidemic. The COST is a mitigation policy that minimizes the peak of the epidemic by providing a constant, optimal allocation of tests in a certain time interval when the total stockpile of tests is limited. Both testing policies are evaluated by their impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths due to COVID-19 in France.

math.OC↗

arXiv2021

A Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE, a Round Trip

In this paper we present a continuation method which transforms spatially distributed ODE systems into continuous PDE. We show that this continuation can be performed both for linear and nonlinear systems, including multidimensional, space- and time-varying systems. When applied to a large-scale network, the continuation provides a PDE describing evolution of continuous state approximation that respects the spatial structure of the original ODE. Our method is illustrated by multiple examples including transport equations, Kuramoto equations and heat diffusion equations. As a main example, we perform the continuation of a Newtonian system of interacting particles and obtain the Euler equations for compressible fluids, thereby providing an original alternative solution to Hilbert's 6th problem. Finally, we leverage our derivation of the Euler equations to control multiagent systems, designing a nonlinear control algorithm for robot formation based on its continuous approximation.

eess.SY↗

arXiv2020

Modeling and Control of Epidemics through Testing Policies

Testing is a crucial control mechanism in the beginning phase of an epidemic when the vaccines are not yet available. It enables the public health authority to detect and isolate the infected cases from the population, thereby limiting the disease transmission to susceptible people. However, despite the significance of testing in epidemic control, the recent literature on the subject lacks a control-theoretic perspective. In this paper, an epidemic model is proposed that incorporates the testing rate as a control input and differentiates the undetected infected from the detected infected cases, who are assumed to be removed from the disease spreading process in the population. After estimating the model on the data corresponding to the beginning phase of COVID-19 in France, two testing policies are proposed: the so-called best-effort strategy for testing (BEST) and constant optimal strategy for testing (COST). The BEST policy is a suppression strategy that provides a minimum testing rate that stops the growth of the epidemic when implemented. The COST policy, on the other hand, is a mitigation strategy that provides an optimal value of testing rate minimizing the peak value of the infected population when the total stockpile of tests is limited. Both testing policies are evaluated by their impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths for the COVID-19 case of France.

math.OC↗