A multigroup SEIR epidemic model with age-dependent latency and relapse

Different multigroup epidemic models have been proposed, but few models include the latent class that becomes infectious at different rates and the fact that the removed class may relapse into an infectious class at different rates. In this paper, a multigroup SEIR epidemic model is constructed to study the transmission dynamics of infectious diseases with age-dependent latency and relapse. The model is realistic for some infectious diseases, such as TB and herpes virus. The sharp threshold condition, which corresponds to the well-known basic reproduction number R0, is derived, and it determines the global stability of each equilibrium. In particular, if R0<1, then the disease-free equilibrium is globally asymptotically stable, whereas if R0>1, the endemic equilibrium exists uniquely and is globally asymptotically stable. We utilize appropriate Lyapunov functionals, graph-theoretical results, and the LaSalle's invariance principle to prove these results. Two specific examples and their corresponding numerical simulations are provided to explain the obtained results.