具有非线性出生率和医院容纳量的传染病模型  

An Epidemic Model with a Nonlinear Birth Rate and Hospital Capacity

作　　者：刘单 刘贤宁[1] LIU Dan;LIU Xianning(School of Mathematics and Statistics, Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2022年第7期35-43,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(12071382).

摘　　要：该文建立并分析了一类具有非线性出生率和医院容纳量的传染病模型.首先,得到了模型解的非负性和有界性.其次,计算基本再生数,并得到了无病平衡点的稳定性.再次,讨论了地方病平衡点的存在情况,并得到了模型发生后向分支的参数条件.分析该参数条件可知,医院收治病人能力越大,后向分支发生的可能性越小.最后,通过数值模拟验证了所得理论结果.In this paper,an infectious disease model with nonlinear birth rate and hospital capacity has been established and analyzed.Firstly,the nonnegativity and boundedness of the model solutions have been obtained.Secondly,the basic reproduction number has been calculated,and the stability of the disease-free equilibrium point been obtained.Thirdly,the existence of the endemic point has been discussed,and the parameter condition for the occurrence of backward bifurcation of the model been obtained.Analysis of the parameter conditions shows that the greater the hospital's ability to admit patients,the less likely the backward bifurcation will occur.Finally,the obtained theoretical results are verified via numerical simulations.

关 键 词：医院容纳量 非线性出生率 后向分支 Lyapunov稳定 

分 类 号：O175[理学—数学]