Dynamics analysis and optimal control of rumor propagation model based on individual cognitive ability

The spread of rumors has a negative impact on the stable development of society. The internal mechanisms, influencing factors, dissemination patterns, and control measures of rumor spreading have always been widely concerned by researchers. In this paper, we consider that the cognitive ability of individuals in society varies, and individual cognitive ability also has a significant effect on rumor spreading, based on which we constructed the SEIR rumor spreading model considering individual cognitive ability. Subsequently, the local and global asymptotic stability of the rumor-free equilibrium and the rumor-existence equilibrium were analyzed. The BASIC reproduction number \({{\boldsymbol{R}}}_0\) of the model was calculated. Finally, considering the optimal control of the system, the individual cognitive ability is taken as the optimal control parameter of the system, and the expression of the optimal control parameter of the system and the optimal control system are given. Numerical simulation supports the results of theoretical analysis and the sensitivity of the system to control parameters. The results of the study show that improving individual cognitive ability can suspend the spread of rumors, enhance the public's reaction time, and then effectively inhibit the spread of rumors.