Nonlinear Dynamical Analysis and Optimal Control Strategies for a New Rumor Spreading Model with Comprehensive Interventions

In the current era, information dissemination is more convenient, the harm of rumors is more serious than ever. At the beginning of 2020, COVID-19 is a biochemical weapon made by a laboratory, which has caused a very bad impact on the world. It is very important to control the spread of these untrue statements to reduce their impact on people's lives. In this paper, a new rumor spreading model with comprehensive interventions (background detection, public education, official debunking, legal punishment) is proposed for qualitative and quantitative analysis. The basic reproduction number with important biological significance is calculated, and the stability of equilibria is proved. Through the optimal control theory, the expression of optimal control pairs is obtained. In the following numerical simulation, the optimal control under 11 control strategies are simulated. Through the data analysis of incremental cost-effectiveness ratio and infection averted ratio of all control strategies, if we consider the control problem from different perspectives, we will get different optimal control strategies. Our results provide a flexible control strategy for the security management department.