Models for transmission of disease with immigration of infectives.
Simple models for disease transmission that include immigration of infective individuals and variable population size are constructed and analyzed. A model with a general contact rate for a disease that confers no immunity admits a unique endemic equilibrium that is globally stable. A model with mass action incidence for a disease in which infectives either die or recover with permanent immunity has the same qualitative behavior. This latter result 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-like results are given, but in the presence of immigration of infectives there is no disease-free equilibrium. A considerable reduction of infectives is suggested by the incorporation of screening and quarantining of infectives in a model for HIV transmission in a prison system.
Brauer
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Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2. brauer@math.ubc.ca
van den Driessche
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D003141:Communicable Diseases / Q000453:epidemiology / Q000635:transmission*; D018562:Disease Transmission, Infectious; D004641:Emigration and Immigration; D015658:HIV Infections / Q000453:epidemiology / Q000635:transmission; D006801:Humans; D008954:Models, Biological; D011330:Prisons