Optimal control of an avian influenza model with multiple time delays in state and control variables

Ting Kang, Qimin Zhang, Haiyan Wang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this paper, we consider an optimal control model governed by a class of delay differential equation, which describe the spread of avian inuenza virus from the poultry to human. We take three control variables into the optimal control model, namely: Slaughtering to the susceptible and infected poultry (u1(t)), educational campaign to the susceptible human population (u2(t)) and treatment to infected population (u3(t)). The model involves two time delays that stand for the incubation periods of avian inuenza virus in the infective poultry and human populations. We derive first order necessary conditions for existence of the optimal control and perform several numerical simulations. Numerical results show that different control strategies have different effects on controlling the outbreak of avian inuenza. At the same time, we discuss the inuence of time delays on objective function and conclude that the spread of avian inuenza will slow down as the time delays increase.

Original languageEnglish (US)
Pages (from-to)4147-4171
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number8
StatePublished - Aug 2021


  • Avian inuenza model
  • Multiple time delays
  • Numerical results
  • Optimal control
  • Stability analysis

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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