We develop a multi-group and multi-patch model to study the effects of population dispersal on the spatial spread of vector-borne diseases across a heterogeneous environment. The movement of host and/or vector is described by Lagrangian approach in which the origin or identity of each individual stays unchanged regardless of movement. The basic reproduction number \(\mathcal {R}_0\) of the model is defined and the strong connectivity of the host-vector network is succinctly characterized by the residence times matrices of hosts and vectors. Furthermore, the definition and criterion of the strong connectivity of general infectious disease networks are given and applied to establish the global stability of the disease-free equilibrium. The global dynamics of the model system are shown to be entirely determined by its basic reproduction number. We then obtain several biologically meaningful upper and lower bounds on the basic reproduction number which are independent or dependent of the residence times matrices. In particular, the heterogeneous mixing of hosts and vectors in a homogeneous environment always increases the basic reproduction number. There is a substantial difference on the upper bound of \(\mathcal {R}_0\) between Lagrangian and Eulerian modeling approaches. When only host movement between two patches is concerned, the subdivision of hosts (more host groups) can lead to a larger basic reproduction number. In addition, we numerically investigate the dependence of the basic reproduction number and the total number of infected hosts on the residence times matrix of hosts, and compare the impact of different vector control strategies on disease transmission.

我们开发了一个多组和多斑块模型来研究人口分散对异质环境中媒介传播疾病空间传播的影响。宿主和/或载体的运动是通过拉格朗日方法描述的，其中每个个体的起源或身份保持不变，无论运动如何。定义了模型的基本再生数\(\mathcal {R}_0\) ，并通过宿主和向量的停留时间矩阵简洁地表征了宿主-向量网络的强连通性。此外，给出了一般传染病网络强连通性的定义和标准，并将其应用于建立无病平衡的全局稳定性。模型系统的全局动态完全由其基本再生数决定。然后，我们获得基本繁殖数的几个具有生物学意义的上限和下限，它们独立于或依赖于停留时间矩阵。特别是，在同质环境中宿主和载体的异质混合总是会增加基本繁殖数。拉格朗日和欧拉建模方法之间的\(\mathcal {R}_0\)上限存在显着差异。当仅考虑两个斑块之间的宿主移动时，宿主的细分（更多的宿主组）可以导致更大的基本繁殖数。此外，我们还通过数值研究了基本繁殖数和受感染宿主总数对宿主停留时间矩阵的依赖性，并比较了不同病媒控制策略对疾病传播的影响。