中文摘要：

对一种具有种群动力和非线性传染率的传染病模型进行了研究,建立了具有常数迁入率和非线性传染率βI~pS~q的SI模型.与以往的具有非线性传染率的传染病模型相比,这种模型引入了种群动力,也就是种群的总数不再为常数,因此,该类模型更精确地描述了传染病传播的规律.还讨论了模型的正不变集,运用微分方程稳定性理论分析了模型平衡点的存在性及稳定性,得出了疾病消除平衡点和地方病平衡点的全局渐进稳定的充分条件.进一步的,得出了在某些参数范围内会出现Hopf分支现象,并对上述模型进行了生物学讨论.

英文摘要：

The paper deals with a kind of epidemic models with population dynamics and non- linear incidence rate.Compared with the former epidemic models with nonlinear incidence rate,an SI epidemic model with nonlinear incidence rate is established,the model introduces population dynam- ics.It means that the total amount of populations is no longer a constant,so this model can describe the communicable diseases transmitting law more accurately.The positive invariant set is discussed, the existence and stability of ...