带有交叉免疫和完全接种的两菌株传染病模型分析(英文)  

Analysis of a Two-strain Epidemic Model with Cross Immunity and Perfect Vaccination

作　　者：李连兵[1] 蔡礼明[1] 李兆强[2] 

机构地区：[1]信阳师范学院数学与信息科学院,河南信阳464000 [2]漯河医学高等专科学校信息中心,河南漯河462002

出　　处：《应用数学》2013年第4期741-749,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11271314);the Natural Science Foundation of Henan Province (13A110759);the University Key Teacher Foundation of Henan Province (2009GGJS-076,2012GGJS-268)

摘　　要：建立一类非线性微分方程系统来描述带有交叉免疫和完全接种两菌株传染病动力学行为.我们得到每种菌株的基本再生数R1(ψ),R2(ψ)和侵入再生数R12,R21表达式,讨论模型中菌株的共存和稳定性.通过数学分析和数值模拟,证明了交叉免疫和完全接种在疾病传播过程中发挥着重要作用.A nonlinear system of different equations that models the dynamics of a two-strain disease with cross immunity and perfect vaccination is formulated. We establish the criteria for determining the coexistence and stability of strains equilibria according to the strain basic reproductive numbers .R1 （φ） and R2 （φ）, and the invasion reproduction numbers R2^1 and R1. Mathematical analysis and simulations show that cross immunity and perfect vaccination play a role in the dynamical behavior of the disease transmission.

关 键 词：两菌株模型 再生数 交叉免疫 完全接种 稳定和共存 

分 类 号：O175[理学—数学]