School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China.
Math Biosci Eng. 2021 Jul 28;18(5):6452-6483. doi: 10.3934/mbe.2021321.
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.
近优控制在理论和应用上都与优化一样合理且重要。本文考虑了具有饱和项的异质复杂网络上禽流感模型的近优控制。首先，为模型定义了基本再生数 $ \mathcal{R}_{0} $，它可用于控制流感疾病的阈值动态。其次，通过宰杀家禽和治疗感染人群来制定近优控制问题，同时使损失和成本最小化。得益于哈密尔顿函数的最大条件和 Ekeland 的变分原理，我们通过对状态和伴随过程的一些精细估计，建立了近优性的充分必要条件。最后，通过一些例子来说明我们的理论结果。
