Bifurcation analysis of an SIS epidemic model with a generalized non-monotonic and saturated incidence rate  

作　　者：Chunxian Huang Zhenkun Jiang Xiaojun Huang Xiaoliang Zhou 

机构地区：[1]School of Mathematics and Statistics Lingnan Normal University,Zhanjiang Guangdong 524048,P.R.China

出　　处：《International Journal of Biomathematics》2024年第4期39-73,共35页生物数学学报（英文版）

基　　金：supported by the NSF of China[Grant No.11961021];the NSF of Guangdong province[Grant Nos.2022A1515010964 and 2022A1515010193];the Innovation and Developing School Project of Guangdong Province[Grant No.2019KzDXM032];the Special Fund of Science and Technology Innovation Strategy of Guangdong Province[Grant Nos.pdjh2022b0320 and pdjh2023b0325].

摘　　要：In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic properties of the model were studied by qualitative theory and bifurcation theory.It is shown that when the infuence of psychological factors is large,the model has only disease-free equilibrium point,and this disease-free equilibrium point is globally asymptotically stable;when the influence of psychological factors is small,for some parameter conditions,the model has a unique endemic equilibrium point,which is a cusp point of co-dimension two,and for other parameter conditions the model has two endemic equilibrium points,one of which could be weak focus or center.In addition,the results of the model undergoing saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation as the parameters vary were also proved.These results shed light on the impact of psychological behavior of susceptible people on the disease transmission.

关 键 词：SIS epidemic model generalized non-monotone and saturated incidence rate saddle-node bifurcation Hopf bifurcation Bogdanov-Takens bifurcation 

分 类 号：O17[理学—数学]