Global stability of multi-group epidemic model with distributed delays and indirect transmission

In this paper, a multi-group epidemic model with distributed delays and indirect transmission is discussed. We identified the basic reproduction number R0 and investigated the dynamical properties of the model with respect to R0. It is proved that the disease-free equilibrium is globally asymptotically stable if R0 ≤ 1, and there exists a unique endemic equilibrium which is globally asymptotically stable if R0 > 1. Specifically, we used the method of Lyapunov functionals and graph-theoretical approach to prove that the global stability of the endemic equilibrium. © 2023 Journal of Nonlinear Functional Analysis.