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We investigate bifurcations and dynamical behaviors of discrete SEIS models with exogenous reinfections and a variety of treatment strategies. Bifurcations identified from the models include period doubling, backward, forward-backward, and multiple backward bifurcations. Multiple attractors, such as bistability and tristability, are observed. We also estimate the ultimate boundary of the infected regardless of initial status. Our rigorously mathematical analysis together with numerical simulations show that epidemiological factors alone can generate complex dynamics, though demographic factors only support simple equilibrium dynamics. Our model analysis supports and urges to treat a fixed percentage of exposed individuals.