Abstract
Immigration has contributed to the increase of certain infectious diseases in some regions. To inspect the impact of controlling immigration of infectious individuals on the transmission of infectious diseases in a region, we construct a basic SIR model with switching imported infectious population. There is no disease-free equilibrium and no basic reproduction number for this system. Based on the global dynamical analysis for the switching system, we know that a proper control of immigration of infectious individuals can control the infectious population for a region at a certain low level.
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