Dynamic Analysis of a SEVIQBR Infectious Disease Model with Media Coverage and Environmental Transmission

Considering the influence of media reports and environmental transmission on disease transmission, a SEVIQBR infectious disease model is established. Firstly, the basic reproduction number ${\mathcal{R}}_0$ of the model is obtained by the next generation matrix method. Based on the basic reproduction number, the existence of disease-free equilibrium and endemic equilibrium of the model is discussed. Then, the local stability of disease-free equilibrium is studied by means of Hurwitz criterion, and the global asymptotic stability of disease-free equilibrium is studied by constructing an appropriate Lyapunov function. The results show that when the basic reproduction number ${\mathcal{R}}_0$ < 1, the disease-free equilibrium of the model is globally asymptotically stable. When ${\mathcal{R}}_0$ satisfies certain conditions, the endemic equilibrium of the model exists. Finally, we give some numerical simulations to explain the theoretical results.