Predicting Mpox outbreaks: the influence of higher-order interactions and temporal network structure on Turing pattern formation

In recent years, the multi-country outbreak and cross-border transmission of Mpox have posed new challenges to the global public health system. This paper constructs a Susceptible-Infective ( S I ) epidemic model based on higher-order temporal network to describe the spatiotemporal transmission dynamics of Mpox virus, and derives the specific criterion of Turing instability. Numerical simulations show that the higher-order temporal network can better reflect the dynamic changes of real crowd contact than the higher-order static network, and significantly improve the authenticity of the model. In terms of the effect of system parameters, mortality, recovery rate and diffusion coefficient of susceptible population S play a leading role in epidemic prevention and control, while the influence of infection rate and diffusion coefficient of infective population I is weak. In addition, periodic diffusion has been shown to significantly promote the formation of Turing patterns and accelerate the system in reaching steady state. As far as the network type is concerned, the scale-free network bifurcates earlier and stabilizes faster than the small-world network, and its key nodes play a decisive role in the pattern and infection peak. Finally, the introduction of 2-simplex can effectively characterize group interaction and strengthen Turing instability. It is worth noting that the simulated annealing algorithm based on the infectious disease system shows better error control and trend capture ability in the validation set, which can be used to simulate the effect of policy intervention and predict the spread trend.