Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

Advances in Difference Equations

article

Yang, Youping¹  Wang, Jingwen¹ 

[1] School of Mathematics and Statistics, Shandong Normal University

关键词: Nonsmooth threshold policy;    Filippov control;    Global stability;    Sliding modes;   

DOI  :  10.1186/s13662-021-03375-z

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY