Feedback control on immigration to reduce spread of infectious diseases with an ISS guarantee

The capability of non-medical strategies to reduce spread of infectious diseases is limited, but evidently quarantining and isolation methods have been effective to slow the transmission. This paper studies regulations on immigration which manipulates the number of individuals entering the area. The immigration including newborns cannot be zero to maintain human societies or ecological systems, but a decision can be made to slow or delay the entering individuals when it is effective to reduce the spread peaks. This paper proposes a feedback control strategy with theoretical guarantees of non-local convergence to the steady state which the society targets. It is proved that small errors in the manipulation of immigration cause only small deviations and they never result in tragedies in terms of input-to-state stability.