Optimal Control of Heterogeneous Mutating Viruses

Elena Gubar, Vladislav Taynitskiy and Quanyan Zhu
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Elena Gubar: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint-Petersburg 198504, Russia
Vladislav Taynitskiy: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii Prospekt 35, Petergof, Saint-Petersburg 198504, Russia
Quanyan Zhu: Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, Brooklyn, NY 11201, USA

Games, 2018, vol. 9, issue 4, 1-18

Abstract: 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.

Keywords: epidemic process; SIR model; optimal control; evolutionary games; virus mutation (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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