Time-dependent optimal control of a SEITR spreading model with hesitation and truth mechanisms

This paper introduces a hesitation mechanism and true information spreaders to establish a Susceptible-Exposed-Infected-Truth-spreader-Recovered (SEITR) rumor propagation model, aiming to reveal how true information spreading influences rumor diffusion. First, based on the Routh-Hurwitz criterion and Lyapunov functions, the local asymptotic stability and global asymptotic stability of the system are proved respectively. Second, the Pontryagin minimum principle is applied to design the optimal control strategy, where key parameters are set as time-dependent functions, and the flexible control of the rumor propagation proportion is realized by dynamically adjusting control variables. Finally, numerical simulations verify the theoretical findings, which show that increasing the true information spreaders and blocking rumor transformation paths can effectively suppress rumor spread.