Global analysis of discrete-time SI and SIS epidemic models

  • Received: 01 February 2007 Accepted: 29 June 2018 Published: 01 August 2007
  • MSC : 92D30, 39A11.

  • 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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  • 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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    © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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