独立生存的两菌株对逼近模型

Approximation Model of Independent Survival Two-Strain

建立了两种菌株生存的对逼近模型,研究了两种菌株独立生存和共存的条件.利用雅可比矩阵证明了无病平衡点的局部稳定性,通过矩阵理论分析特征值的相关方法得到了与两菌株相对应的基本再生数的表达式,进而得到边界平衡点及正平衡点存在的条件.最后选取适当的模型参数利用Matlab进行了计算机模拟,验证了边界平衡点及正平衡点的稳定性.

An approximation model with two strains was established and the condition of independent existence and coexistence was studied. By using jacobian matrix proved the local stability of the diseasefree equilibrium point, and obtained the corresponding expressions of the basic reproductive number through matrix theory analysing of the characteristic values, then the existence conditions of boundary equilibrium and positive equilibrium was obtained. It is verified that the boundary equilibrium and the positive equilibrium point is stable through the Matlab computer simulation by choosing appropriate model parameters.