Stability and Hopf bifurcation of a delayed epidemic model with stage structure and nonlinear incidence rate (Q2922246)

Let \(S_1(t)\) be the the density of immature population at time \(t\), \(S_2(t)\) and \(I(t)\) be the densities of susceptible and infectious mature populations at time \(t\), respectively. Assume that the disease spreads only among the mature population. The author considers an epidemic model composed by the above three groups, which is a delayed SI model with stage structure and nonlinear incidence rate \(g(I)+\frac{\beta I}{1+\alpha I}\). Firstly, the basic reproduction number \(R_0\) is obtained, and the equilibria, local stability and Hopf bifurcation are analyzed by the characteristic equation method. Then the global stability of the endemic equilibrium and the disease-free equilibrium are proved by an iteration technique. Some numerical simulation are given to illustrate the applications of the established results.