Department of Mathematics and Statistics, Cleveland State University, Cleveland, 44115, OH, USA.
Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China.
J Math Biol. 2024 Jan 31;88(2):22. doi: 10.1007/s00285-023-02044-x.
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 [Formula: see text] 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 [Formula: see text] 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.
我们开发了一个多群体和多斑块模型，以研究种群扩散对异质环境中媒介传播疾病空间传播的影响。宿主和/或媒介的运动采用拉格朗日方法描述，其中每个个体的起源或身份保持不变，无论其运动如何。模型的基本繁殖数[Formula: see text]被定义，并且宿主-媒介网络的强连通性通过宿主和媒介的居留时间矩阵简洁地刻画。此外，给出了一般传染病网络的强连通性的定义和准则，并将其应用于建立无病平衡点的全局稳定性。模型系统的全局动力学完全由其基本繁殖数决定。然后，我们得到了几个关于基本繁殖数的有生物学意义的上界和下界，它们独立或依赖于居留时间矩阵。特别地，在同质环境中宿主和媒介的异质混合总是增加基本繁殖数。拉格朗日和欧拉建模方法之间在[Formula: see text]的上限上存在显著差异。当仅考虑两个斑块之间的宿主运动时，宿主的细分（更多的宿主群体）会导致更大的基本繁殖数。此外，我们数值研究了基本繁殖数和受感染宿主总数对宿主居留时间矩阵的依赖关系，并比较了不同媒介控制策略对疾病传播的影响。
