Analysis of transmission dynamics of dengue fever on a partially degenerated weighted network

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.