Dynamics and optimal control of a weighted-network dengue model with seasonal transmission

In this paper, we introduce a novel dengue model on a weighted network to investigate the roles of human mobility, seasonal temperature shifts, and spatial heterogeneity. First, the positivity, global existence, and ultimate boundedness of the model solutions have also been discussed. Then, by utilizing the next generation operator theory, we derived the basic reproduction number $R_0$ for the model, which determines the threshold dynamics of the system: When $R_0<1$ , the model possesses a unique disease-free periodic solution that is globally asymptotically stable; whereas when $R_0>1$ , dengue fever persists in both humans and mosquitoes, with at least one endemic periodic solution existing. Moreover, we formulate a corresponding optimal control model for dengue disease and derive the optimal prevention strategies with minimal implementation costs. Finally, several numerical examples are conducted to validate the theoretical results and the visualization outcomes demonstrate that spatial heterogeneity leads to heterogeneous disease transmission, and the total number of infected humans and infected mosquitoes increasing as the diffusion rate of infected humans rises and the peak of the temperature difference in the season is greater, and the epidemic is more likely to break out earlier, with more infected humans and mosquitoes. Additionally, we also present the control effects under different combinations of control measures and the spatiotemporal evolution of the optimal control solution.