In this paper, we propose a partially degenerated weighted network dynamical model for dengue fever transmission to study its spatial transmission dynamics, in which population mobility are characterized by the weighted graph Laplacian diffusion. Firstly, we establish the comparison principle for general reaction–diffusion differential equations defined on finite weighted network. Next, the well-posedness of solutions is established for the model. Then the basic reproduction number of the model is calculated, and then the stability of disease-free and endemic equilibria is investigated by means of the upper and lower solutions method and the construction of Lyapunov function. Furthermore, the uniform persistence of the model also is demonstrated. Finally, we apply the generalized weighted graph to the Watts–Strogatz network and present several numerical examples to verify theoretical results and obtain some interesting conclusions: the peak numbers of infected human population and infected mosquito populations depending on the node degree, even though the equations for the mosquito population in the model has no diffusion term.

中文翻译：

---

登革热在部分退化加权网络上的传播动力学分析


在本文中，我们提出了一个用于登革热传播的部分退化加权网络动力学模型来研究其空间传播动力学，其中人口流动性由加权图 Laplacian 扩散表征。首先，我们建立了在有限加权网络上定义的一般反应-扩散微分方程的比较原则。接下来，为模型建立解的适定性。然后计算模型的基本繁殖数，然后通过上下解法和 Lyapunov 函数的构造研究无病平衡和地方性均衡的稳定性。此外，还证明了模型的均匀持久性。最后，我们将广义加权图应用于 Watts-Strogatz 网络，并提供了几个数值示例来验证理论结果并获得一些有趣的结论：感染人口和感染蚊子种群的峰值数量取决于节点程度，即使模型中蚊子种群的方程没有扩散项。