A multi-scale mathematical model of rumor propagation considering both intra- and inter-individual dynamics

The widespread propagation of rumors has become a serious challenge today, posing a serious threat to public trust and social stability. To comprehensively examine the dynamics of rumor propagation, in this paper, we propose a multi-scale mathematical model that couples the intra-individual information discrimination process and the inter-individual rumor propagation process using nested modeling approach. Subsequently, we conduct a detailed mathematical analysis of the intra-and inter-individual dynamics process to obtain the basic regeneration number and the equilibrium points of the systems, respectively, and then prove the stability of the equilibrium point by using the Lyapunov stability theory. Numerical simulations reveal that during the initial stages of rumor propagation, individuals are more likely to be converted into spreaders due to their insufficient knowledge reserves. Enhancing the learning ability of individuals can enable individuals to identify rumors more quickly and transform into stiflers, thus reducing the scale of rumor propagation. In addition, we find that the greater the heterogeneity in the rumor's retention duration in the information base, i.e., the more scattered the time of rumor uploading by spreaders, which makes the rumor keep emerging in the information base, the wider the scale of rumor propagation will be. In addition, we find that the greater the heterogeneity in the rumor's retention duration in the information base, i.e., the more scattered the time of rumor uploading by spreaders, the wider the scale of rumor propagation will be. This is because rumors are constantly emerging in the information base. It is worth noting that the decreasing trend in the popularity of the rumor gradually slows down, which indicates that the effect of intervening on the rumor at the early stage of propagation is more significant.