社会经济领域中一类扩散现象的数学模型

利用数学模型讨论社会经济现象中两类群体在互动中的扩散现象规律，指出这种现象是否保持取决于内增长率，当内增长率小于零时，扩散现象消除的平衡点总存在，并且这个平衡点全局渐近稳定，从而扩散现象逐渐消失，当内增长率大于零时，这个平衡点变得不稳定，但保持扩散现象的平衡点存在惟一，在平衡点，当两类群体人数相等时，它们的接触率与感染率相同，由此推出当内增长率大于零时，扩散现象保持，且在一定条件下有惟一的吸引子。

Mathematical model of a diffusion phenomenon in social-economic region

A diffusion phenomenon in the interaction of two communities is discussed through mathematical methods and it is pointed out that the kind of phenomenon is decided by the intrinsic growth rate. When the intrinsic growth rate is less than zero, the disease free equilibrium of the model exists, and it is global asymptotic stable. So the kind of phenomenon disappears gradually. When the intrinsic growth rate is larger than zero, the disease free equilibrium of the model is not stable, and an only epidemic equilibrium of the model exists. At the equilibrium point, the contact rate is equal to the infection rate when the number of two communities are equal. Thus the kind of phenomenon keeps and there is a unique attractor under certain condition.