一类STD模型的竞争熄灭与共存

研究了一种存在于异性活动人群中的,通过性活动进行传播的病菌所构成的系统.在这个系统中,女性被分成N-1个不同的群体,而根据传播能力的不同,病原体菌株被分成两类.对这种系统,讨论了其地方病平衡点以及边界平衡点的稳定性,得到了这些平衡点存在及稳定的充分必要条件.结果确认,在边界平衡点的稳定性和地方病平衡点的存在性之间存在强烈的联系,即地方病平衡点存在当且仅当地方病平衡点同时存在并且具有相同的稳定性.

Competitive exclusion and coexistence of a class of sexually-transmitted disease models

The dynamics of sexually transmitted pathogens in a heterosexually active population was studied, where females were divided into N-1 different groups based on their susceptibility to two distinct pathogenic strains. The coexistence and stability of that boundary equilibria was investigated, and the sufficient and necessary conditions for the existence and stability of these equilibria were obtained. It was verified that there is a strong connection between the stability of boundary equilibria and the existence of the coexistence equilibrium, that is, there exists at least one coexistence equilibrium if and only if the boundary equilibria both exist and have the same stability.