Gao Daozhou, van den Driessche P, Cosner Chris
Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China.
Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 2Y2, Canada.
J Math Biol. 2019 Dec;79(6-7):2255-2280. doi: 10.1007/s00285-019-01428-2. Epub 2019 Sep 13.
Based on a Ross-Macdonald type model with a number of identical patches, we study the role of the movement of humans and/or mosquitoes on the persistence of malaria and many other vector-borne diseases. By using a theorem on line-sum symmetric matrices, we establish an eigenvalue inequality on the product of a class of nonnegative matrices and then apply it to prove that the basic reproduction number of the multipatch model is always greater than or equal to that of the single patch model. Biologically, this means that habitat fragmentation or patchiness promotes disease outbreaks and intensifies disease persistence. The risk of infection is minimized when the distribution of mosquitoes is proportional to that of humans. Numerical examples for the two-patch submodel are given to investigate how the multipatch reproduction number varies with human and/or mosquito movement. The reproduction number can surpass any given value whenever an appropriate travel pattern is chosen. Fast human and/or mosquito movement decreases the infection risk, but may increase the total number of infected humans.
基于一个具有多个相同斑块的罗斯 - 麦克唐纳类型模型，我们研究了人类和/或蚊子的移动对疟疾及许多其他媒介传播疾病持续存在的作用。通过使用关于线和对称矩阵的一个定理，我们建立了一类非负矩阵乘积的特征值不等式，然后应用它来证明多斑块模型的基本再生数总是大于或等于单斑块模型的基本再生数。从生物学角度来看，这意味着栖息地破碎化或斑块化会促进疾病爆发并加剧疾病的持续存在。当蚊子的分布与人类的分布成比例时，感染风险最小化。给出了双斑块子模型的数值例子，以研究多斑块再生数如何随人类和/或蚊子的移动而变化。只要选择合适的移动模式，再生数可以超过任何给定值。人类和/或蚊子的快速移动会降低感染风险，但可能会增加感染人类的总数。
