Global analysis of a new reaction–diffusion multi-group SVEIR propagation model with time delay

In this work, the global dynamic behavior of a new reaction–diffusion multi-group SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) rumor propagation model is studied. Compared with the traditional SVIR and SEIR models, the new model takes into account the latent of rumors, that is, believing rumors does not mean spreading rumors, and the impact of official rumor refutation on rumor propagation, which will lead to positive changes in the results of rumor propagation. The expression of 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} obtained through the next generation matrix method. By constructing Lyapunov function and applying graph-theoretic approach, we have obtained that the rumor eliminating equilibrium point E0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E_0$$\end{document} is globally asymptotically stable when R0≤1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0\le 1$$\end{document}, and the rumor spreading equilibrium point E∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E^*$$\end{document} is globally asymptotically stable when R0>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0>1$$\end{document}. The conclusion is verified by numerical simulation. In addition, the effects of time delay and the total number of plates are also given by numerical simulation.