Global dynamics of the multi-lingual SIR rumor spreading model with cross-transmitted mechanism. (English) Zbl 1448.91220
Summary: 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.
MSC:
| 91D30 | Social networks; opinion dynamics |
| 34D05 | Asymptotic properties of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
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