Dynamical analysis and optimal control of the developed information transmission model

Information transmission significantly impacts social stability and technological advancement. This paper compares the phenomenon of "Super transmission" and "Asymptomatic infection" in COVID-19 transmission to information transmission. The former is similar to authoritative information transmission individuals, whereas the latter is similar to individuals with low acceptance in information transmission. It then constructs an S2EIR model with transmitter authority and individual acceptance levels. Then, it analyzes the asymptotic stability of information-free and information-existence equilibrium on a local and global scale, as well as the model's basic reproduction number, R0. Distinguished with traditional studies, the population density function and Hamiltonian function are constructed by taking proportion of "Super transmitter" and proportion of hesitant group turning into transmitters as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively facilitate information transmission. The numerical simulation corroborates the theoretical analysis results and the system's sensitivity to control parameter changes. The research results indicate that the authoritative "Super transmitter" has a beneficial effect on information transmission. In contrast, the "Asymptomatic infected individual" with poor individual acceptance level negatively affects information transmission.