Gourley Stephen A, Liu Rongsong, Wu Jianhong
Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK.
J Math Biol. 2007 Mar;54(3):309-35. doi: 10.1007/s00285-006-0050-x. Epub 2006 Nov 17.
We derive appropriate mathematical models to assess the effectiveness of culling as a tool to eradicate vector-borne diseases. The model, focused on the culling strategies determined by the stages during the development of the vector, becomes either a system of autonomous delay differential equations with impulses (in the case where the adult vector is subject to culling) or a system of nonautonomous delay differential equations where the time-varying coefficients are determined by the culling times and rates (in the case where only the immature vector is subject to culling). Sufficient conditions are derived to ensure eradication of the disease, and simulations are provided to compare the effectiveness of larvicides and insecticide sprays for the control of West Nile virus. We show that eradication of vector-borne diseases is possible by culling the vector at either the immature or the mature phase, even though the size of the vector is oscillating and above a certain level.
我们推导了适当的数学模型，以评估扑杀作为根除媒介传播疾病工具的有效性。该模型侧重于由病媒发育阶段决定的扑杀策略，在成年病媒接受扑杀的情况下，成为一个具有脉冲的自治延迟微分方程组；在仅未成熟病媒接受扑杀的情况下，成为一个非自治延迟微分方程组，其时变系数由扑杀时间和速率决定。推导了确保疾病根除的充分条件，并进行了模拟，以比较杀幼虫剂和杀虫剂喷雾对控制西尼罗河病毒的有效性。我们表明，即使病媒数量在波动且高于一定水平，在未成熟或成熟阶段扑杀病媒也有可能根除媒介传播疾病。
