Analysis of rumor spreading with different usage ranges in a multilingual environment

This paper investigates rumor propagation in a multilingual environment, taking into account language usage variations. Firstly, a 2I2S2R model is proposed within a heterogeneous network framework that incorporates both immunologic and cross-transmitted mechanisms. Secondly, the paper calculates the basic reproduction number $R_0$ by the next-generation matrix method. Thirdly, the local asymptotic stability and the global asymptotic stability are further explored, which indicate that whether the rumor continuously spreads or becomes extinct is determined by the threshold. Finally, the numerical simulation and sensitivity analysis are given to illustrate the effectiveness of theoretical results and the influence of model parameters on rumor spreading.