Free-riding is a common phenomenon in the knowledge transmission process. Compared with acquiring knowledge from individual interactions, acquiring knowledge from a knowledge base can be regarded as a free-riding behavior that costs less and benefits from team contributions. To consider this approach in knowledge infection modeling, in this study, a heterogeneous stochastic susceptible–infected-recovered (SSIR)-knowledge base (B) knowledge transmission model is established, based on the similarity between water-borne diseases and knowledge transmission considering free-riding. Specifically, a “water pool” (i.e., a knowledge base) is associated with the individual interactions, to describe how knowledge can travel from groups to free riders. The model includes two knowledge infection processes: human–human infection and human–knowledge base–human infection. As a difference from the waterborne disease model, these two processes act on active and free riders, respectively. A theoretical basic regeneration number is given. Furthermore, the global stabilities of the knowledge-free equilibrium and knowledge-endemic equilibrium are analyzed. The theoretical analysis implies that when $R_0<1$, the knowledge in the system will eventually die out. Conversely, when $R_0>1$, knowledge transmission will remain active. Numerical simulations are used to illustrate the theoretical analysis results, and can be used to further investigate the effects of parameters on the knowledge propagation process. The results suggest that our model can provide a good mechanism for two different understandings about free-riding.

搭便车是知识传播过程中的普遍现象。与从个人交互中获取知识相比，从知识库中获取知识可以被认为是一种搭便车的行为，其花费更少，受益于团队的贡献。为了在知识感染建模中考虑这种方法，在本研究中，基于水传播疾病与知识传播之间的相似性（考虑了免费），建立了一种非均质的随机易感感染恢复（SSIR）-知识基础（B）知识传播模型。 -骑术。具体而言，“水库”（即知识库）与个体互动相关联，以描述知识如何从群体传播到自由骑手。该模型包括两个知识感染过程：人与人之间的感染和人与基础知识之间的感染。与水传播疾病模型不同的是，这两个过程分别作用于主动和自由骑手。给出了理论上的基本再生数。此外，分析了无知识均衡和知识地方均衡的全局稳定性。理论分析表明${\mathrm{[R}}_0<\mathrm{1个}$，系统中的知识最终将消失。相反，当${\mathrm{[R}}_0>\mathrm{1个}$，知识传递将保持活跃。数值模拟可用于说明理论分析结果，并可用于进一步研究参数对知识传播过程的影响。结果表明，我们的模型可以为搭便车的两种不同理解提供良好的机制。