How to control the immigration of infectious individuals for a region?

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.