Injurious information propagation and its global stability considering activity and normalized recovering rate.

This paper establishes a compartment model describing the propagation of injurious information among a well-mixed population. We define the information's injuriousness as the people practicing the information being injured and leaving the system. Some informed people practice the information and are active, while others do not practice and are inactive. With the recovery resources fixed, the two groups of informed people's recovering rates are normalized considering the information features. The stability of the nonlinear system is thoroughly studied. Analyzing the reproduction number of the injurious information, we find that in general parameter space, when there are people in an informed compartment, it is not always necessary to consider their recovery resource allocation. Instead, only when their proportion reaches a critical point should it be allocated. Unless the people in an informed compartment form a certain proportion, we can take a laissez-faire attitude towards them. In a more realistic parameter space, once inactive informed people exist, they should be allocated recovery resources. On the one hand, when the recovering rate rises, the focus on both groups of informed people is necessary for more situations. On the other hand, when the rate of active informed people leaving the system rises, ignoring active informed people benefits removing the injurious information in more cases. The model provides qualitative ways in the scenarios of removing injurious information.