Simplicial SAIQS Propagation Model Considering the Influence of Information

为揭示信息影响下的传染病传播规律并探寻防控策略，本研究构建了单纯形–易感–意识–感染–隔离–易感(s-SAIQS)模型。该模型同时考虑出生死亡、高阶相互作用、信息意识及隔离措施等要素，从理论层面证明模型解的有界性与不变集，得到平衡点存在条件与稳定性判据。数值模拟显示，提升有效信息总量、延长信息有效时长，可有效防控传染病；出生率上升、死亡率下降会增加感染者密度并降低流行阈值；隔离措施对抑制感染者密度效果显著，相较于信息意识、出生死亡等因素，其控制作用更为突出。To reveal the transmission patterns of infectious diseases influenced by information and explore prevention and control strategies, this study constructs the simplicial-susceptible-aware-infected-quarantined-susceptible (s-SAIQS) model. This model takes into account elements such as birth and death, high-order interactions, information awareness, and quarantine measures simultaneously. From a theoretical perspective, it proves the boundedness of the model solutions and the invariant set, and obtains the existence conditions of equilibrium points and the criteria for stability. Numerical simulations show that increasing the total amount of effective information and extending the effective duration of information can effectively prevent and control infectious diseases; an increase in the birth rate and a decrease in the death rate will increase the density of infected individuals and reduce the epidemic threshold; quarantine measures have a significant effect on suppressing the density of infected individuals, and their control effect is more prominent compared with factors such as information awareness, birth, and death.