Abstract
In this paper, under the multi-lingual environment, a new ILSR rumor spreading model is firstly proposed, combining with the incubation mechanism, cross-transmitted mechanism and general nonlinear spreading rate. Firstly, the basic reproduction number are obtained by using the next-generation matrix method. Secondly, the global stability of ILSR rumor spreading model are analysed in the bi-lingual environment via using Lyapunov functions and graph theories. Further, the results are extended to the multi-lingual environment. Moreover, an optimal control method is proposed by using Pontryagin’s maximum principle, which can achieve high control effect with low cost. Finally, the correctness of theoretical results is verified by numerical simulation of several models with classical nonlinear spreading rate, such as the saturated spreading rate, the non-monotone spreading rate and so on.
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