Dynamic Analysis and Optimal Control of Rumor Propagation Model with Reporting Effect

Media reports and the number of rumors in the media have an important impact on the spread of rumors. Currently, studies that consider these two factors comprehensively on rumor propagation are uncommon. It is better to consider both effects comprehensively than to consider one of them alone. In this paper, we established a new propagation model, which regards the number of rumors in the media as a subclass that changes with time, and then comprehensively considered the effect of these two factors on the process of rumor propagation. We proved the existence and stability of equilibrium points of the model. Then, we selected two reasonable control variables: science popularization intensity and punishment intensity. We find that the control effects are optimal when these two control variables take the maximum value. Theoretical analysis and numerical simulation results showed that positive media publicity can reduce the spread of rumors, but cannot stop the spread of rumors. And under the parameters given in this paper, the optimal control parameter values satisfying the constraints can be calculated through quantitative analysis. This method provided a new idea for studying the optimal control of rumor propagation.