Bifurcation and optimal control for an infectious disease model with the impact of information  

作　　者：Zhihui Ma Shenghua Li Shuyan Han 

机构地区：[1]School of Mathematics and Statistics Lanzhou University,Lanzhou Gansu 730000,P.R.China

出　　处：《International Journal of Biomathematics》2024年第1期113-149,共37页生物数学学报（英文版）

摘　　要：A nonlinear infectious disease model with information-influenced vaccination behavior and contact patterns is proposed in this paper,and the impact of information related to disease prevalence on increasing vaccination coverage and reducing disease incidence during the outbreak is considered.First,we perform the analysis for the existence of equilibria and the stability properties of the proposed model.In particular,the geometric approach is used to obtain the sufficient condition which guarantees the global asymptotic stability of the unique endemic equilibrium Ee when the basic reproduction number Ro>1.Second,mathematical derivation combined with numerical simulation shows the existence of the double Hopf bifurcation around Ee.Third,based on the numerical results,it is shown that the information coverage and the average information delay may lead to more complex dynamical behaviors.Finally,the optimal control problem is established with information-infuenced vaccination and treatment as control variables.The corresponding optimal paths are obtained analytically by using Pontryagin's maximum principle,and the applicability and validity of virous intervention strategies for the proposed controls are presented by numerical experiments.

关 键 词：Infectious disease model information index STABILITY double Hopf bifurcation optimal control Pontryagin's maximum principle 

分 类 号：O17[理学—数学]