Dynamic analysis of an SSvEIQR model with nonlinear contact rate, isolation rate and vaccination rate dependent on media coverage

In this paper, we study an SS_vEIQR model with nonlinear contact rate, isolation rate and vaccination rate driven by media coverage. First, the basic reproduction number $R_0$ is derived. Then, the threshold dynamics of the disease are obtained in terms of $R_0$: when $R_0\le 1$, the global stability of the disease-free equilibrium is obtained by constructing an appropriate Lyapunov function; when $R_0>1$, the sufficient conditions to prove the globally stability of endemic equilibrium are obtained by applying the geometric method into the four-dimensional system, which needs to estimate the Lozinski$ǐ$ measure of a $6\times 6$ matrix. Further, we conduct some numerical simulations to validate our theoretical results, and analyze the impact of media coverage on disease transmission, the results show that media coverage could effectively suppress the spread of the disease and reduce the number of infected individuals. Finally, through the sensitivity analysis of $R_0$, we obtain some measures to control the spread of the disease, such as reducing contact, strengthening isolation and vaccination.