Depopulation of birds has been authenticated to be an effective measure in controlling avian influenza transmission. In this work, we establish a Filippov avian-only model incorporating a threshold policy control. We choose the index—the maximum between the infected threshold level \(I_{T}\) and the product of the number of susceptible birds S and a ratio threshold value ξ—to decide on whether to trigger the control measures or not, which then leads to a discontinuous separation line and two pieces of sliding-mode domains. Meanwhile, one more sliding-mode domain gives birth to more complex dynamics. We investigate the global dynamical behavior of the Filippov model, including the real and/or virtual equilibria and the two sliding modes and their dynamics. The solutions will eventually stabilize at the real endemic equilibrium of the subsystem or the pseudoequilibria on the two sliding modes due to different threshold values. Therefore an effective and efficient threshold policy is essential to control the influenza by driving the number of infected birds below a certain level or at a previously given level.

鸟类的减少已被证实是控制禽流感传播的有效措施。在这项工作中，我们建立了包含阈值策略控制的Filippov禽类唯一模型。我们选择指数，即感染阈值水平\（I_ {T} \）与易感鸟类数量S与比率阈值ξ的乘积之间的最大值—决定是否触发控制措施，这将导致不连续的分隔线和两个滑模域。同时，另外一个滑模域催生了更复杂的动力学。我们研究了Filippov模型的全局动力学行为，包括真实和/或虚拟平衡以及两个滑动模式及其动力学。由于阈值不同，解决方案最终将稳定在子系统的实际流行平衡或两个滑模上的伪平衡。因此，有效而有效的门槛政策对于通过将感染禽鸟的数量控制在一定水平以下或预先确定的水平以下来控制流感至关重要。