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Games 2018, 9(4), 103;

Optimal Control of Heterogeneous Mutating Viruses

1,†, 1,*,† and 2,†
Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint-Petersburg 198504, Russia
Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 25 August 2018 / Revised: 25 November 2018 / Accepted: 7 December 2018 / Published: 13 December 2018
(This article belongs to the Special Issue Game Models for Cyber-Physical Infrastructures)
PDF [448 KB, uploaded 18 December 2018]


Different strains of influenza viruses spread in human populations during every epidemic season. As the size of an infected population increases, the virus can mutate itself and grow in strength. The traditional epidemic SIR model does not capture virus mutations and, hence, the model is not sufficient to study epidemics where the virus mutates at the same time as it spreads. In this work, we establish a novel framework to study the epidemic process with mutations of influenza viruses, which couples the SIR model with replicator dynamics used for describing virus mutations. We formulated an optimal control problem to study the optimal strategies for medical treatment and quarantine decisions. We obtained structural results for the optimal strategies and used numerical examples to corroborate our results. View Full-Text
Keywords: epidemic process; SIR model; optimal control; evolutionary games; virus mutation epidemic process; SIR model; optimal control; evolutionary games; virus mutation

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Gubar, E.; Taynitskiy, V.; Zhu, Q. Optimal Control of Heterogeneous Mutating Viruses. Games 2018, 9, 103.

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