Global analysis of discrete-time SI and SIS epidemic models
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Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051
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Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049
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Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2
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Received:
01 February 2007
Accepted:
29 June 2018
Published:
01 August 2007
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MSC :
92D30, 39A11.
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Discrete-time SI and SIS models formulated as
the discretization of a continuous-time model may exhibit behavior
different from that of the continuous-time model such as
period-doubling and chaotic behavior unless the step size in the model
is sufficiently small. Some new discrete-time SI and
SIS epidemic models with vital dynamics are formulated and analyzed.
These new models do not exhibit period doubling and chaotic
behavior and are thus better approximations to continuous models. However,
their reproduction numbers and therefore their asymptotic behavior can differ
somewhat from that of the corresponding continuous-time model.
Citation: Jianquan Li, Zhien Ma, Fred Brauer. Global analysis of discrete-time SI and SIS epidemic models[J]. Mathematical Biosciences and Engineering, 2007, 4(4): 699-710. doi: 10.3934/mbe.2007.4.699
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Abstract
Discrete-time SI and SIS models formulated as
the discretization of a continuous-time model may exhibit behavior
different from that of the continuous-time model such as
period-doubling and chaotic behavior unless the step size in the model
is sufficiently small. Some new discrete-time SI and
SIS epidemic models with vital dynamics are formulated and analyzed.
These new models do not exhibit period doubling and chaotic
behavior and are thus better approximations to continuous models. However,
their reproduction numbers and therefore their asymptotic behavior can differ
somewhat from that of the corresponding continuous-time model.
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