HIV与免疫响应动力学的时间-空间模型(英文)

A spatiotemporal model for HIV and immune response dynamics

致力于通过使用偏微分方程来描述及刻画HIV病毒、易感染细胞、免疫细胞三者之间的动态免疫响应的时间-空间模型.该模型由3个反应-扩散方程来描述,利用微分不等式技巧以及嵌入定理证明了全局解的存在惟一性,利用常微分方程中解的稳定性理论方法证明了常数稳态解的稳定性,并且通过严格的数学分析证明了非常数稳态解的不存在性,并得出了该模型可以由常微分方程的方法来刻画的结论.

A spatiotemporal model for HIV and immune response dynamics was described by three reaction-diffusion partial differential equations. The global existence and uniqueness of classical solutions to this model was proved by the method of applications of partial differential inequality and embedding theory. And the nonlinear stability of constant solutions was studied by means of stability theorem of the ordinary differential equation. Furthermore, the nonexistence of non-constant steady states was also discussed by rigorous mathematical analysis. The rigorous mathematical analysis of this paper shows that the corresponding simpler ordinary differential equation （ODE） model was a good approximation to above-mentioned PDE model.