Dynamical analysis of a stochastic rumor-spreading model with Holling II functional response function and time delay

Xiaomin Chen,Liang’An Huo

doi:10.1186/s13662-020-03096-9

Abstract

With the rapid development of information society, rumor plays an increasingly crucial part in social communication, and its spreading has a significant impact on human life. In this paper, a stochastic rumor-spreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise is proposed. Firstly, the existence of a unique global positive solution of the model is studied. Then the asymptotic behavior of the global solution around the rumor-free and rumor-local equilibrium nodes of the deterministic system is discussed. Finally, through some numerical results, the validity and availability of theoretical analysis is verified powerfully, and it shows that some factors such as the transmission rate, the intensity of white noise, and the time delay have significant relationship with the dynamical behavior of rumor spreading.

Highlights

1 Introduction Rumor spreading has had a significant impact on human life, especially in the modern era of Internet, there is no geographical limit to rumor spreading, which brings much wider and faster spreading
On the basis of the deterministic model considering the Holling II functional response function and time delay, we take the stochastic disturbance into consideration so that we can better grasp the dynamic properties
7 Conclusions This paper is mainly related to the dynamical properties of a stochastic SIR rumorspreading model with Holling II functional response function considering the existence of time delay and the disturbance of white noise

Summary

Introduction

Rumor spreading has had a significant impact on human life, especially in the modern era of Internet, there is no geographical limit to rumor spreading, which brings much wider and faster spreading. A rumor-spreading model only considering unilateral factor is far from adequate, both the time delay of thinking and the external disturbance from media or government, etc., may exert great influence on the dynamic behavior of this model. We establish a rumor spreading model which takes Holling II functional response function, time delay, and stochastic disturbance into consideration simultaneously, it could be further accord with practical situation and grasp the dynamic characteristic of rumor spreading more precisely. 2, we propose a stochastic SIR rumor-spreading model with Holling II functional response function and time delay. On the basis of the deterministic model considering the Holling II functional response function and time delay, we take the stochastic disturbance into consideration so that we can better grasp the dynamic properties.

The dynamic properties around the rumor-free equilibrium

Conclusions