Open AccessGlobal analysis of discrete-time SI and SIS epidemic models
Author(s) -
Jianquan Li,
Zhien Ma,
Fred Brauer
Publication year - 2007
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2007.4.699
Subject(s) - chaotic , discretization , discrete time and continuous time , period doubling bifurcation , mathematics , continuous modelling , statistical physics , computer science , mathematical analysis , nonlinear system , statistics , bifurcation , physics , quantum mechanics , artificial intelligence
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.