Dynamical analysis of a [formula omitted] epidemic-like propagation model with non-smooth control

Abstract

The continuous acceleration of information communication makes the spread of rumors constantly develop and change. Analysis of the dynamics of rumor propagation allows for its better control. In this paper, we study a rumor transmission model with a nonlinear transmission rate and a non-smooth threshold transmission function, based on the classical SI infectious disease model. In this model, we first prove the existence of the model solutions, and then obtain the number of non-negative equilibrium points. By dividing the model into spatially homogeneous and inhomogeneous parts with continuous and discontinuous, we discuss the characteristic equations of the equilibrium points and obtain the existence conditions for Saddle–node bifurcation, Turing bifurcation and Hopf bifurcation under the corresponding conditions. Finally, the feasibility of the theoretical calculation results is further verified by using the simulation results.