【摘要】 针对HIV/AIDS传播的具有常数移民和指数出生的SI型模型,为了更加符合实际意义,对具有双线性传染率的模型进行局部改进,并对改进后的动力学模型进行了简化.对于改进后的模型,证明了平衡点的存在与局部稳定性,并证明了传染病毒的灭绝与持续性,得到了传染病毒的基本再生数.结果表明:当单位时间内从外界迁入人口中染病者的比例系数c近似等于零时,基本再生数小于1时,传染病毒最终灭绝;当基本再生数大于1时,模型存在唯一的正平衡点,且是局部渐近稳定的,说明传染病毒一致持续存在.更多还原

【Abstract】 In order to fit realistic meaning,the model of the Si-type models of HIV/AIDS transmission with a constant immigration and a exponential birth with the bilinear infection ratio are locally modified and simplified in this paper.For the improved model,existence of equilibrium and local stablility are proved,and the extiction of virus and persistence are showed.The basic reproduction ratio is gained.The results show that the virus will be extinct ultimately when the scale c,which is the ratio of the infected people to the whole population with moving from the outside in the unit time,is closed to zero and the basic reproduction is less than one.And when the basic production is greater than one the model has a unique positive equilibrium which is locally asymptotically stable.This implies the virus will persist in host.更多还原