Global analysis of discrete-time SI and SIS epidemic models - Jianquan Li; Zhien Ma; Fred Brauer (Mathematical Biosciences and Engineering)
Discrete-time SI and SIS models formulated asthe discretization of a continuous-time model may exhibit behaviordifferent from that of the continuous-time model such asperiod-doubling and chaotic behavior unless the step size in the modelis sufficiently small. Some new discrete-time SI andSIS epidemic models with vital dynamics are formulated and analyzed.These new models do not exhibit period doubling and chaoticbehavior and are thus better approximations to continuous models. However,their reproduction numbers and therefore their asymptotic behavior can differsomewhat from that of the corresponding continuous-time model.