Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 39, Issue 11-12, Pages 1231-1242Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2004.06.004
Keywords
epidemic models; vaccination; global stability; threshold
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Epidemic models of SIS type without vaccination and with vaccination are analyzed to determine the thresholds, equilibria, and stabilities. The vaccinations have two different formulations. One of SIS models with vaccination is a delay differential equation, another is an ordinary differential equation. For the delay differential equation, the asymptotic behavior is globally asymptotically stable convergence to a disease-free equilibrium, below the threshold, and to an endemic equilibrium, above a threshold. For the ordinary differential equations, the asymptotic behavior is globally asymptotically stable convergence to a disease-free equilibrium below the threshold, the sufficient conditions of the globally asymptotically stable convergence to an endemic equilibrium are obtained above the threshold, and the endemic equilibrium is locally asymptotically stable above the threshold. (C) 2004 Elsevier Ltd. All rights reserved.
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