Modeling of knowledge transmission by considering the level of forgetfulness in complex networks

• Knowledge forgetfulness is an inevitable phenomenon, which depends on the quantity of neighboring spreaders.
• The level of forgetfulness is given a new interpretation, which can be understood as a special function of spreaders.
• The number of spreaders increases asymptotically when a better cultural atmosphere exists.

In this study, we establish a general model by considering the level of forgetfulness during knowledge transmission in complex networks, where the level of forgetfulness depends mainly on the number in a crowd who possess knowledge, while the saturated incidence is also considered. In theory, we analyze the stability of the equilibrium points and the transmission threshold R0R0 is also given. If R0>1R0>1, then knowledge can ​be transmitted, but if not, it will become completely extinct. In addition, we performed some numerical simulations to verify the reasonability of the theoretical analysis. The results of the simulations also suggest ​that the proportion of the crowd with knowledge will be increased under a better cultural atmosphere.