Seasonality is pervasive in nature and WNV is a complex disease which appears to be transmitted periodically. Lacking of vaccine and anti-virus treatment brings culling to be an effective strategy of controlling the spread of WNV. This paper proposes a piecewise smooth model of WNV transmission between mosquitoes and birds with periodic forcing by employing the threshold policy of culling mosquitoes and birds when the number of infected birds exceeds the critical level. We firstly investigate the dynamical behaviours of the periodic subsystems and illustrate the existence and global stability of the disease-free and positive periodic solutions. Then by assuming a periodic variation in the total number of mosquitoes and birds with and without culling strategy respectively in the ecosystem, the subsystems are reduced, respectively. Further, the sliding mode domain and sliding mode dynamics are derived by using the Filippov convex method and the existence of the sliding periodic solution is illustrated. Finally, numerical investigations are carried out to address how the periodic forcing and culling strategy affect the pattern and amplitude of the novel periodic solution. Our results show that a suitable combination of threshold value and culling rates should be properly chosen to ensure that the ideal periodic solution with a low number of infected birds/mosquitoes oscillating in a small range is globally stable and consequently is approximated, which suggests useful strategies of curbing WNV transmission by setting proper threshold level and culling rates.

季节性本质上无处不在，WNV是一种复杂的疾病，似乎定期传播。缺乏疫苗和抗病毒治疗使淘汰成为控制WNV传播的有效策略。提出了一种在被感染鸟类数量超过临界水平时，采用扑杀蚊子和鸟类的阈值策略，采用周期性强迫的分段平滑WNV传播模型。我们首先研究周期子系统的动力学行为，并说明无病的正周期解的存在性和全局稳定性。然后，通过假设生态系统中分别采用和不采用淘汰策略的蚊子和鸟类总数的周期性变化，分别减少了子系统。进一步，利用Filippov凸方法推导了滑模域和滑模动力学，并说明了滑模周期解的存在性。最后，进行了数值研究，以解决周期性强迫和剔除策略如何影响新型周期解的模式和幅度。我们的研究结果表明，阈值和淘汰率的适当组合应正确选择，以保证具有低的被感染的鸟类/蚊子在小范围内振荡的理想周期解是全局稳定的，因此近似，这表明有用的策略通过设置适当的阈值水平和剔除率来抑制WNV传播。