具Holling-III型治疗函数的SEIR模型及其稳定性分析

Stability Analysis of a SEIR Model with Holling-III Therapeutic Function

利用常微分方程定性与稳定性分析理论研究了一类具Holling-III型治疗函数的SEIR传染病模型,给出了基本再生数的定义,分析了模型的正定性,有界性以及无病平衡点的局部渐近稳定性,并判断了地方病平衡点局部渐近稳定需满足的条件。最后通过数值模拟验证了理论分析结果。

Using the theory of ordinary differential equation qualitative and stability analysis to study SEIR epidemic model with Holling-III treatment function,the definition of the basic reproductive number is given,the positive definiteness,boundedness and the locally asymptotic stability of the disease-free equilibrium of the model are analyzed,and the locally asymptotically stable endemic equilibrium conditions to be fulfilled are presented.Finally,the results of theoretical analysis are verified by numerical simulation.