Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism

Abstract

• Under the multi-lingual environment, a new SIR rumor spreading model, which divides the population with different languages into distinct groups, is first proposed in this paper. Meanwhile, the dynamical behaviors are systematically studied based on the Lyapunov function, graph-theoretic approach and uniform persistence theory. • To further illustrate the influence of model parameters on the rumor spreading, we evaluate the sensitivity index of the basic reproduction number and analyze how crucial each parameter is to the rumor transmission and prevalence. • Since the rumor assumed in this paper can cross-transmit between different groups, the results obtained here are more general and practical compared with the existing papers [11,12,14,16]. The dynamical behaviors of the multi-lingual SIR rumor spreading model are investigated in this paper. In view of the actual background, we consider the rumor spreading under the multi-lingual environment, and further establish a new model with cross-transmitted mechanism. Employing the theory of infectious diseases, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. In addition, the global asymptotic stability of endemic equilibrium of the proposed model is analyzed via applying Lyapunov functions and graph theories. In addition, we perform sensitivity analysis on threshold conditions to determine the relative importance of model parameters to rumor transmission. Finally, the effectiveness of theoretical results is illustrated through the numerical examples.