An epidemiological model with a delay and a nonlinear incidence rate |
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| Authors: | H. W. Hethcote M. A. Lewis P. van den Driessche |
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| Affiliation: | (1) Department of Mathematics, University of Iowa, 52242 Iowa City, IA, USA;(2) Centre for Mathematical Biology, Mathematical Institute, 24-29 St. Giles, OX1 3LB Oxford, UK;(3) Department of Mathematics, University of Victoria, V8W 2Y2, B.C., Canada |
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| Abstract: | An epidemiological model with both a time delay in the removed class and a nonlinear incidence rate is analysed to determine the equilibria and their stability. This model is for diseases where individuals are first susceptible, then infected, then removed with temporary immunity and then susceptible again when they lose their immunity. There are multiple equilibria for some parameter values, and, for certain of these, periodic solutions arise by Hopf bifurcation from the large nontrivial equilibrium state.Research supported in parts by Centers for Disease Control Contract 200-87-0515Research supported in part by NSERC A-8965 |
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| Keywords: | Epidemiological model Hopf bifurcation Nonlinear incidence Time delay |
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