Dynamic analysis and control of the spatiotemporal epidemic diffusion model driven by higher-order temporal networks

Information plays a crucial role in the prevention and management of infectious diseases, but it can also potentially accelerate their spread. This study constructs multiple higher-order networks based on existing complex networks. We construct a higher-order temporal multiplex network that integrates information diffusion and epidemic spreading, based on the Unaware–Aware–Unaware–Susceptible–Exposed–Infected–Recovered–Susceptible ($UAU$-$SEIRS$) framework, to accurately describe the dynamic processes of information propagation and epidemic spreading. Additionally, we derive an expression for the epidemic threshold to determine the critical conditions for the epidemic outbreak. Higher-order interactions in the information dissemination layer increase the epidemic threshold, while higher-order interactions in the epidemic spread layer decrease the epidemic threshold. We further consider births and deaths and construct a $SEIRS$ higher-order spatiotemporal network dynamics system. Subsequently, we investigate the Turing instability criteria in the higher-order system to study the pattern formation mechanisms of epidemic spreading in space. Adding lower-order interactions and reducing the order of the coupling function leads to Turing instability. The definition of the higher-order adjacency matrix and the generation method of higher-order networks significantly influence the distribution of infected individuals. Additionally, we propose an optimal control strategy under resource constraints aimed at effectively controlling epidemic spreading by adjusting isolation measures and verify its effectiveness in delaying epidemic spread. Finally, the $SEIRS$ system can effectively accommodate China’s cumulative monkeypox infection data.