中文摘要：

研究一类具有非线性传染率βI^PS/1＋αI^P的流行病模型,模型中引入了种群动力.运用微分方程定性理论讨论了模型的正不变集,分析了该系统疾病消除平衡点和地方病平衡点的存在性及稳定性,得出了全局渐近稳定的充分条件.最后对上述模型进行了生物学讨论.

英文摘要：

In this paper,a class of epidemic models with nonlinear incidence rate βI^PS/1＋αI^PP is studied,where we introduce population dynamics.The positive invariant set of the model is discussed by using qualitative theory of differential equations,and the existence and stability of the endemic steady state and the disease-free steady state are analyzed.We obtain the sufficient conditions for the global asymptotic stability of the models.Finally the biological significance is discussed.