Global stability and Hopf bifurcation of networked respiratory disease model with delay

Time delay is introduced into a networked respiratory disease model, which describes the occurrence of respiratory diseases caused by air pollution. By analyzing the eigenvalues, it has been proven that when the delay exceeds the threshold, the endemic equilibrium loses stability through Hopf bifurcation. In addition, employing Lyapunov functions, we provide the condition that the endemic equilibrium is globally asymptotically stable. Our work extends the stability theory of the classical networked delayed reaction-diffusion model.