具有常数迁入率和非线性传染率βI~pS~q的SI模型分析

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.

SI epidemic model with constant input and nonlinear incidence rate

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 the equilibrium point are analyzed by stability theory of ordinary dif- ferential equations,and the conditions for global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are obtained.Farther,for some range of parameters there can exist Hopf bifurcation.