Mathematical Biosciences and Engineering (MBE)

Global analysis of discrete-time SI and SIS epidemic models

Pages: 699 - 710, Volume 4, Issue 4, October 2007      doi:10.3934/mbe.2007.4.699

       Abstract        Full Text (173.5K)       Related Articles

Jianquan Li - Department of Applied Mathematics and Physics, Air Force Engineering University, Xi'an 710051, China (email)
Zhien Ma - Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China (email)
Fred Brauer - Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada (email)

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.

Keywords:  discrete-time epidemic model, dynamic behavior, equilibrium, stability.
Mathematics Subject Classification:  92D30, 39A11.

Received: February 2007;      Accepted: July 2007;      Available Online: August 2007.