Application of Promotion Process Based on Epidemic Models Considering Bidirectionality

Abstract

In this paper, on the basis of previous epidemic models, we considered the bidirectionality of a certain process of the model and established the Ignorant, Exposers, Resister of product, Supporter of product, Uninterested (IERSU) model, and applied it to a new field. Firstly, the next generation matrix method was used to obtain the threshold parameter which helps to distinguish the equilibrium point of the model. Secondly, the local and global stability of the equilibrium point of the model were proved by the judgment and properties of the negative definite matrix, Lyapunov's first method and LaSalle's invariance principle. Finally, according to the numerical simulation, the influence of different parameters of the model was analyzed and a series of strategies were discussed.