https://doi.org/10.1140/epjp/s13360-023-03698-8
Regular Article
Global analysis of a fractional-order reaction-diffusion rumor-spreading model in multi-lingual environment
1
College of Mathematics and System Sciences, Xinjiang University, 830046, Urumqi, China
2
School of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China
Received:
1
November
2022
Accepted:
10
January
2023
Published online:
30
January
2023
In this paper, a fractional-order reaction-diffusion rumor propagation model in multi-lingual environment is established. The boundedness of the model’s solution is obtained. Further, it can be seen that the dynamic behavior of the model’s solution is affected by the threshold 
, which can be calculated by the next generation matrix method. In addition, the global asymptotic stability of equilibrium is discussed by means of Lyapunov function method. Furthermore, the importance of parameters in the threshold is evaluated by means of sensitivity analysis. Finally, several numerical simulation examples are given to verify the correctness of the corresponding theoretical results.
This work is funded by the National Natural Science Foundation of China under Grant 62163035, by the Special Project for Local Science and Technology Development Guided by the Central Government under Grant ZYYD2022A05, by the Xinjiang Key Laboratory of Applied Mathematics under Grant XJDX1401, by the Natural Science Foundation of Xinjiang Uygur Autonomous Region under Grant 2021D01C113.
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