Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Global analysis of discrete-time SI and SIS epidemic models

1. Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051
2. Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049
3. Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords discrete-time epidemic model; dynamic behavior; equilibrium; stability.

Citation: Jianquan Li, Zhien Ma, Fred Brauer. Global analysis of discrete-time SI and SIS epidemic models. Mathematical Biosciences and Engineering, 2007, 4(4): 699-710. doi: 10.3934/mbe.2007.4.699

 

This article has been cited by

  • 1. Qamar Din, Qualitative behavior of a discrete SIR epidemic model, International Journal of Biomathematics, 2016, 09, 06, 1650092, 10.1142/S1793524516500923
  • 2. Tailei Zhang, Junli Liu, Zhidong Teng, Threshold conditions for a discrete nonautonomous SIRS model, Mathematical Methods in the Applied Sciences, 2015, 38, 9, 1781, 10.1002/mma.3186
  • 3. Guirong Jiang, Qigui Yang, Periodic solutions and bifurcation in an SIS epidemic model with birth pulses, Mathematical and Computer Modelling, 2009, 50, 3-4, 498, 10.1016/j.mcm.2009.04.021
  • 4. Zengyun Hu, Zhidong Teng, Long Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model, Mathematics and Computers in Simulation, 2014, 97, 80, 10.1016/j.matcom.2013.08.008
  • 5. Zhidong Teng, Lei Wang, Linfei Nie, Global attractivity for a class of delayed discrete SIRS epidemic models with general nonlinear incidence, Mathematical Methods in the Applied Sciences, 2015, 38, 18, 4741, 10.1002/mma.3389
  • 6. Zengyun Hu, Zhidong Teng, Haijun Jiang, Stability analysis in a class of discrete SIRS epidemic models, Nonlinear Analysis: Real World Applications, 2012, 13, 5, 2017, 10.1016/j.nonrwa.2011.12.024
  • 7. Soodeh Hosseini, Mohammad Abdollahi Azgomi, Adel Torkaman Rahmani, Malware propagation modeling considering software diversity and immunization, Journal of Computational Science, 2016, 13, 49, 10.1016/j.jocs.2016.01.002
  • 8. Jahangir Chowdhury, Sourav Rana, Sabyasachi Bhattacharya, Priti Kumar Roy, , Industrial Mathematics and Complex Systems, 2017, Chapter 23, 319, 10.1007/978-981-10-3758-0_23
  • 9. Yoichi Enatsu, Yukihiko Nakata, Yoshiaki Muroya, Global stability for a discrete SIS epidemic model with immigration of infectives, Journal of Difference Equations and Applications, 2012, 18, 11, 1913, 10.1080/10236198.2011.602973
  • 10. Lei Wang, Zhidong Teng, Haijun Jiang, Global attractivity of a discrete SIRS epidemic model with standard incidence rate, Mathematical Methods in the Applied Sciences, 2013, 36, 5, 601, 10.1002/mma.2734
  • 11. Tailei Zhang, Permanence and extinction in a nonautonomous discrete SIRVS epidemic model with vaccination, Applied Mathematics and Computation, 2015, 271, 716, 10.1016/j.amc.2015.09.071
  • 12. Zengyun Hu, Linlin Chang, Zhidong Teng, Xi Chen, Bifurcation analysis of a discrete S I R S ${SIRS}$ epidemic model with standard incidence rate, Advances in Difference Equations, 2016, 2016, 1, 10.1186/s13662-016-0874-7
  • 13. JUPING ZHANG, ZHEN JIN, DISCRETE TIME SI AND SIS EPIDEMIC MODELS WITH VERTICAL TRANSMISSION, Journal of Biological Systems, 2009, 17, 02, 201, 10.1142/S0218339009002788

Reader Comments

your name: *   your email: *  

Copyright Info: 2007, , licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved