具有不同非线性发病率的两菌株模型分析  

A two-strain epidemic model with different nonlinear incidences rates

作　　者：任亚鑫 薛亚奎[1] REN Yaxin;XUE Yakui(School of Science, North University of China, Taiyuan 030051, China)

机构地区：[1]中北大学理学院,太原030051

出　　处：《重庆理工大学学报（自然科学）》2022年第6期282-290,共9页Journal of Chongqing University of Technology：Natural Science

基　　金：国家自然科学青年基金项目(11301491);山西省自然科学青年基金项目(2018010221040);山西“1331”工程重点创新团队。

摘　　要：为深入了解疾病传播机制,研究了具有不同非线性发病率的两菌株传染病模型。确定了模型的4个平衡点,得到了2个基本再生数R_(0)^(1)和R_(0)^(2)。借助Lyapunov函数的方法证明了当R_(0)^(2)≤1时,若R_(0)^(1)≤1则两菌株消亡,若R_(0)^(1)>1则菌株1持续及菌株2消亡。当R_(0)^(2)>1时,在特定条件下,若R_(0)^(1)≤1则菌株1消亡及菌株2持续,若R_(0)^(1)>1则两菌株持续。数值模拟支持了分析结果,表明了研究疾病的发病率对防控疾病的重要性。In order to gain insights into the mechanism of epidemic transmission,an epidemic model describing two-strain with different nonlinear incidence rates is studied.Four equilibrium points of the model are found and the basic reproduction numbers R_(0)^(1) and R_(0)^(2) are obtained.By means of Lyapunov function,it is proved that when R_(0)^(2)≤1,if R_(0)^(1)≤1,the both strains die out,and if R_(0)^(1)>1,the strain 1 persists and the strain 2 dies out,while when R_(0)^(2)>1,under specific conditions,if R_(0)^(1)≤1,the strain 1 dies out and the strain 2 persists,and if R_(0)^(1)>1,the both strains persist.Numerical simulations support the results of the analysis and demonstrate the importance of studying the incidence of diseases for disease prevention and control.

关 键 词：非线性发病率 两菌株 LYAPUNOV函数 全局稳定性分析 

分 类 号：O175[理学—数学]