Open AccessNear-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks
Author(s) -
Keguo Ren,
Xining Li,
Qimin Zhang
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021321
Subject(s) - optimal control , hamiltonian (control theory) , influenza a virus subtype h5n1 , mathematical optimization , maximum principle , mathematics , control (management) , basic reproduction number , computer science , biology , artificial intelligence , virology , medicine , population , virus , environmental health
Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns the near-optimal control of an avian influenza model with saturation on heterogeneous complex networks. Firstly, the basic reproduction number $ \mathcal{R}_{0} $ is defined for the model, which can be used to govern the threshold dynamics of influenza disease. Secondly, the near-optimal control problem was formulated by slaughtering poultry and treating infected humans while keeping the loss and cost to a minimum. Thanks to the maximum condition of the Hamiltonian function and the Ekeland's variational principle, we establish both necessary and sufficient conditions for the near-optimality by several delicate estimates for the state and adjoint processes. Finally, a number of examples presented to illustrate our theoretical results.