Dynamic analysis of a novel SI network rumour propagation model with self-regulatory mechanism

In our modern world, rumours have triggered chaos and conflicts. Study of the dynamics of rumor propagation helps yield effective countermeasures to resist rumour propagation. It is a major task to study an ordinary differential equation (ODE) model on high-order incidence and treatment function for its dynamical behaviours. First and foremost, we build an ODE model depending on the actual transmission mechanism. Secondly, we study the basic properties of solutions including non-negativity, boundedness and situation of inexistence of the limit cycle. Thirdly, we study the necessary conditions of the equilibrium points for the existence, stability and instability. Furthermore, this study analyses bifurcations induced by parameters around the equilibrium point of rumour-spreading. Finally, several numerical simulations are given to show diverse dynamics behaviours of the model on different parameters and the factors affecting rumour propagation are theoretically analysed, which proves the validity of the theoretical analysis.