Qualitative theory of differential equations describing dynamics of infectious disease

我们得到了一些关于描述宿主中感染源的动力学的微分方程模型的定性性质的结果。在这里，我们讨论了病毒、靶细胞、感染细胞和免疫之间的相互作用。对于某些模型，我们证明了对应于感染状态的内部平衡点在一定条件下是全局渐近稳定的。在这方面，我们考虑了免疫的一些数学模型，并建立了描述自身免疫的微分方程组的一些性质。

We obtained some results on qualitative properties of differential equation models describing the dynamics of infectious agents in a host. Here we dealt with the interaction among viruses, target cells, infected cells, and immunity. We showed for some models that the interior equilibrium, which corresponds to the infected state, is, under some conditions, globally asymptotically stable. In this connection, we considered some mathematical models of immunity, and established some properties of systems of differential equations describing autoimmunity.