一类带有扩散和B-D反应项的病毒模型的稳定性分析

Asymptotic Stability of a Viral Dynamics Model with Diffusion and B-D Functional Responses

本文研究了齐次Neumann边界条件下带有扩散和B-D反应项病毒模型的平衡解渐近稳定性.利用弱耦合抛物不等式组的最大值原理,给出了模型解的先验估计.利用赫尔维茨(Hurwitz)定理,分析了平衡解的局部渐近稳定性.结果表明:当基本再生数大于1时,地方病平衡态局部渐近稳定;当基本再生数小于1时,无病平衡态局部渐近稳定.同时,利用构造上下解及其单调迭代序列的方法证明了无病平衡解的全局渐近稳定性,该结果表明:当控制细胞生成率或者感染率或者感染细胞裂解率充分小时,无病平衡解的全局渐近稳定.

A viral dynamics model with diffusion and B-D functional response under homo-geneous Neumann boundary condition is investigated in this paper, in which the stabilities of equilibria are analyzed. A priori estimate is proved by the maximum principle of the coupled parabolic inequalities. Based on the Hurwitz theorem, it is proved that the endemic equilibrium is locally stable when the basic reproductive number is greater than one and the disease-free equilibrium is locally stable when it is less than one. Furthermore, through constructing upper and lower solutions to the problem and establishing its associated monotone iterative sequences, we prove the global stability of the disease-free solution. The result shows that if the recruit-ment rate or the contact rate of the susceptible population or the resolution ratio of the infected compartment is small enough, the disease-free solution is globally stable.