### Mathematical Biosciences and Engineering

2021, Issue 5: 6452-6483. doi: 10.3934/mbe.2021321
Research article

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

• 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.

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

### Related Papers:

• 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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沈阳化工大学材料科学与工程学院 沈阳 110142

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