Complex dynamics of a discrete-time SIR model with nonlinear incidence and recovery rates  

作　　者：Xiao Yu Ming Liu Zhaowen Zheng Dongpo Hu 

机构地区：[1]School of Mathematical Sciences Qufu Normal University Qufu 273165,P.R.China

出　　处：《International Journal of Biomathematics》2023年第8期1-45,共45页生物数学学报（英文版）

基　　金：supported by the NSF of Shandong Province(ZR2021MA016,ZR2019MA034,ZR2018BF018);the China Postdoctoral Science Foundation(2019M652349);the Youth Creative Team Sci-Tech Program of Shandong Universities(2019KJI007).

摘　　要：In this paper,a discrete-time SIR epidemic model with nonlinear incidence and recovery rates is obtained by using the forward Euler’s method.The existence and stability of fixed points in this model are well studied.The center manifold theorem and bifurcation theory are applied to analyze the bifurcation properties by using the discrete time step and the intervention level as control parameters.We discuss in detail some codimension-one bifurcations such as transcritical,period-doubling and Neimark–Sacker bifurcations,and a codimension-two bifurcation with 1:2 resonance.In addition,the phase portraits,bifurcation diagrams and maximum Lyapunov exponent diagrams are drawn to verify the correctness of our theoretical analysis.It is found that the numerical results are consistent with the theoretical analysis.More interestingly,we also found other bifurcations in the model during the numerical simulation,such as codimension-two bifurcations with 1:1 resonance,1:3 resonance and 1:4 resonance,generalized period-doubling and fold-flip bifurcations.The results show that the dynamics of the discrete-time model are richer than that of the continuous-time SIR epidemic model.Such a discrete-time model may not only be widely used to detect the pathogenesis of infectious diseases,but also make a great contribution to the prevention and control of infectious diseases.

关 键 词：Discrete-time SIR epidemic model nonlinear incidence rate nonlinear recovery rate codimension-one bifurcation codimension-two bifurcation 

分 类 号：O175[理学—数学]