Deciphering dengue fever transmission on higher-order networks.

Dengue fever is a viral infection transmitted to humans through the bites of infected mosquitoes. Modeling dengue transmission is crucial for control, given its risk to half the world's population. This paper develops a host-to-host transmission model within hypergraphs constructed from simplicial complexes. Necessary conditions for the emergence of Turing instability in dengue dynamical systems naturally coupled on hypergraphs are derived. Furthermore, a multiplex network framework is constructed on hypergraphs by incorporating the influence of information on dengue transmission, and expressions for dengue outbreak thresholds are derived. Theoretical results are verified through numerical simulations. The Turing instability phenomenon in higher-order networks is investigated, while periodic diffusion effects are analyzed. Higher-order networks elevate the thresholds for dengue outbreaks within the multiplex network framework. Finally, to link theory with practice, we employ Physics-Informed Neural Networks (PINNs) to fit and predict dengue case data. By embedding the transmission model as physical constraints and constructing hypergraphs informed by geographical adjacency and tourism mobility, the PINNs achieves interpretable predictions and accurate parameter estimation. This study offers a feasible framework for understanding and predicting dengue transmission in complex real-world environments.