Two SIS epidemiologic models with delays |
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Authors: | Herbert W Hethcote P van den Driessche |
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Institution: | (1) Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA, US;(2) Department of Mathematics and Statistics, University of Victoria, Victoria, B.C. V8W 3P4, Canada, CA |
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Abstract: | The SIS epidemiologic models have a delay corresponding to the infectious period, and disease-related deaths, so that the
population size is variable. The population dynamics structures are either logistic or recruitment with natural deaths. Here
the thresholds and equilibria are determined, and stabilities are examined. In a similar SIS model with exponential population
dynamics, the delay destabilized the endemic equilibrium and led to periodic solutions. In the model with logistic dynamics,
periodic solutions in the infectious fraction can occur as the population approaches extinction for a small set of parameter
values.
Received: 10 January 1997 / 18 November 1997 |
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Keywords: | : Epidemiologic modeling – SIS model – Delay – Threshold – Hopf bifurcation |
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