Optimal control of heterogeneous mutating viruses

Elena Gubar, Vladislav Taynitskiy, Quanyan Zhu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number103
Issue number4
StatePublished - Dec 1 2018


  • Epidemic process
  • Evolutionary games
  • Optimal control
  • SIR model
  • Virus mutation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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