The conjecture of Arino and van den Driessche (Citation2003) that a SIS type model in a mover-stayer epidemic model is globally asymptotically stable is confirmed analytically. If the basic reproduction number , then the disease-free equilibrium is globally asymptotically stable. If , then there exists a unique endemic equilibrium that is globally asymptotically stable on the nonnegative orthant minus the stable manifold of the disease-free equilibrium.
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Iggidr et al. (2012) studied this question.
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