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In this paper, we investigate a class of multi-group epidemic models with general exposed distribution and nonlinear incidence rate. Under biologi- cally motivated assumptions, we show that the global dynamics are completely determined by the basic production number R0. The disease-free equilibrium is globally asymptotically stable if R0 1, and there exists a unique endem- ic equilibrium which is globally asymptotically stable if R0 > 1. The proofs of the main results exploit the persistence theory in dynamical system and a graph-theoretical approach to the method of Lyapunov functionals. A simpler case that assumes an identical natural death rate for all groups and a gam- ma distribution for exposed distribution is also considered. In addition, two numerical examples are showed to illustrate the results.

GLOBAL DYNAMICS IN A MULTI-GROUP EPIDEMIC MODEL FOR DISEASE WITH LATENCY SPREADING AND NONLINEAR TRANSMISSION RATE