Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks

Keguo Ren; Xining Li; Qimin Zhang; Keguo Ren; Xining Li; Qimin Zhang

doi:10.3934/mbe.2021321

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 5: 6452-6483. doi: 10.3934/mbe.2021321

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Research article

Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks

1.
School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China
2.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China

Academic Editor: Tonghua Zhang

Received: 19 May 2021 Accepted: 23 July 2021 Published: 28 July 2021

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.
- complex networks,
- avian influenza model,
- spatial diffusion,
- near-optimal control,
- basic reproduction number
Citation: Keguo Ren, Xining Li, Qimin Zhang. Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks[J]. Mathematical Biosciences and Engineering, 2021, 18(5): 6452-6483. doi: 10.3934/mbe.2021321

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Abstract

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.

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