Chong Nyuk Sian, Dionne Benoit, Smith Robert
Department of Mathematics and Statistics, University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada.
School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030, Kuala Terengganu, Malaysia.
J Math Biol. 2016 Sep;73(3):751-84. doi: 10.1007/s00285-016-0971-y. Epub 2016 Feb 10.
Depopulation of birds has always been an effective method not only to control the transmission of avian influenza in bird populations but also to eliminate influenza viruses. We introduce a Filippov avian-only model with culling of susceptible and/or infected birds. For each susceptible threshold level [Formula: see text], we derive the phase portrait for the dynamical system as we vary the infected threshold level [Formula: see text], focusing on the existence of endemic states; the endemic states are represented by real equilibria, pseudoequilibria and pseudo-attractors. We show generically that all solutions of this model will approach one of the endemic states. Our results suggest that the spread of avian influenza in bird populations is tolerable if the trajectories converge to the equilibrium point that lies in the region below the threshold level [Formula: see text] or if they converge to one of the pseudoequilibria or a pseudo-attractor on the surface of discontinuity. However, we have to cull birds whenever the solution of this model converges to an equilibrium point that lies in the region above the threshold level [Formula: see text] in order to control the outbreak. Hence a good threshold policy is required to combat bird flu successfully and to prevent overkilling birds.
鸟类种群数量减少一直是一种有效的方法，不仅可以控制禽流感在鸟类种群中的传播，还能消灭流感病毒。我们引入了一个仅针对鸟类的菲利波夫模型，该模型对易感和/或感染鸟类进行扑杀。对于每个易感阈值水平[公式：见原文]，当我们改变感染阈值水平[公式：见原文]时，我们推导了动态系统的相图，重点关注地方病状态的存在；地方病状态由实际平衡点、伪平衡点和伪吸引子表示。我们一般地表明，该模型的所有解都将趋近于其中一个地方病状态。我们的结果表明，如果轨迹收敛到位于阈值水平[公式：见原文]以下区域的平衡点，或者如果它们收敛到不连续面上的伪平衡点或伪吸引子之一，那么禽流感在鸟类种群中的传播是可以容忍的。然而，为了控制疫情爆发，每当该模型的解收敛到位于阈值水平[公式：见原文]以上区域的平衡点时，我们都必须扑杀鸟类。因此，需要一个良好的阈值策略来成功抗击禽流感并防止过度捕杀鸟类。
