Models for transmission of disease with immigration of infectives

Simple models for disease transmission that include immigration of infectiv e individuals and variable population size are constructed and analyzed. A model with a general contact rate for a disease that confers no immunity ad mits a unique endemic equilibrium that is globally stable. A model with mas s action incidence for a disease in which infectives either die or recover with permanent immunity has the same qualitative behavior. This latter resu lt is proved by reducing the system to an integro-differential equation. If mass action incidence is replaced by a general contact rate, then the same result is proved locally for a disease that causes fatalities, Threshold-l ike results are given, but in the presence of immigration of infectives the re is no disease-free equilibrium. A considerable reduction of infectives i s suggested by the incorporation of screening and quarantining of infective s in a model for HIV transmission in a prison system. (C) 2001 Published by Elsevier Science Inc.