An adaptive resource allocation mechanism based on patch cluster structures: Coupling resource flow and epidemic spreading dynamics in metapopulation networks

Epidemic outbreaks threaten global health and stability, creating an urgent need for effective resource allocation strategies. Existing studies often neglect dynamic regional risk adjustments and resource coordination based on cluster structures. To address this, this paper proposes an adaptive resource allocation mechanism based on the patch cluster structures and develops a coupled dynamics model that integrates resource flow with epidemic spreading in a metapopulation network. The model employs a migration-interaction-return process to characterize both inter-patch migration and intra-patch epidemic spreading. Furthermore, an adaptive resource allocation mechanism is designed, which dynamically adjusts both inter-patch donation strategies and intra-cluster allocation schemes according to evolving, patch-specific risk levels, thereby realizing dynamic optimization of resource distribution. Using the micro Markov chain approach, we derive epidemic evolution equations and calculate infection thresholds. Numerical simulations validate the model and examine key parameter impacts. The results show that increasing patch cluster numbers, enhancing inter-cluster connectivity, and improving cluster efficiency-especially in networks with abundant triangular structures-effectively raise the epidemic threshold and reduce infection scale. Compared to traditional models, adaptive resource allocation models can utilize resources more efficiently, thereby decreasing the infection scale. Higher donation/utilization rates mitigate global spread, while targeted assistance from high-risk to low-risk patches lowers overall prevalence. This study provides a theoretical framework for dynamic group resource optimization in heterogeneous risk environments, offering valuable insights for epidemic prevention and control.