具有功能性反应的自免疫疾病模型的稳定性分析
Stability Analysis of Autoimmune Disease Model with Functional Response
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摘要: 利用Lyapunov函数方法和LaSalle不变集原理研究了带有Holling-Tanner第Ⅱ类功能性型反应的自免疫疾病动力学模型的全局稳定性. 当基本再生数R0≤1, 病毒在体内清除; 而R0＞1时, 病毒在体内持续生存. 利用Routh-Hurwitz 原理研究了带有Holling-Tanner第Ⅲ类功能性反应的自免疫疾病动力学模型的局部稳定性.Abstract: In this paper, we propose a mathematical model for autoimmune disease with functional response of immune cells to target cells. It is found that virus persists in the host if the basic reproductive ratio of the virus is greater than 1. The global properties of a model with Holling-Tanner type Ⅱ functional response are studied using Lyapunov functions and LaSalles invariance principle, and conditions for stability of positive equilibrium of the system with Holling-Tanner type Ⅲ functional response are analyzed using Routh-Hurwitz criteria.
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