Dynamic analysis and optimal control considering cross transmission and variation of information

Cross-transmission of information has a profound influence on the progress of science and technology and the discipline integration in the field of education. In this work, knowledge gained from the viral recombination and variation in COVID-19 transmission is applied to information transmission. Virus recombination and virus variation are similar to the crossing and information fusion phenomena in information transmission. An S2I4MR model with information crossing and variation is constructed. Then, the local and global asymptotic stabilities of the information-free equilibrium and information-existence equilibrium are analyzed. Additionally, the basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0$$\end{document} of the model is calculated. As such, an optimal control strategy is hereby proposed to promote the cross-transmission of information and generate variant information. The numerical simulations support the results of the theoretical analysis and the sensitivity of the system towards certain control parameters. In particular, the results show that strengthening information crossing promotes the generation of variant information. Furthermore, encouraging information exchange and enhancing education improve the generation of information crossing and information variation.