【摘要】 把SEIS传染病模型中的普遍双线性传染率改变为非线性传染率,同时改变SEIS模型中单一的常数输入人口A,使其以比例q划分,输入人口中qA为潜伏者,(1-q)A为易感者.针对改变后的模型,对系统正不变集内的疾病平衡点进行讨论,给出了在系统正不变集内决定疾病持续存在的基本再生数R1.得出传染病系统存在唯一地方病平衡点的充要条件是R1>1,并利用Liapunov函数证明了该地方病平衡点是全局渐近稳定的.讨论了改变常数输入A之后的传染病模型不存在疾病灭绝的无病平衡点,以及q变化时对模型中平衡点中各因素的影响.更多还原

【Abstract】 Change the incidence rate of SEIS epidemic model from βSI to nonlinear,and change the inflows A with the proportionality factor q:qA is the number of exposed individuals while(1-q)A is the number of susceptible individuals.It is showed that the global dynamics and the outcome of the disease are completely determined by the basic reproduction number R1;there is a unique endemic equilibrium if and only if R1>1.In addition,when 0<q<1 and R1>1,the unique endemic equilibrium is proved to be locally asymptotically stable by using Liapunov function.In the end,it is proved that there is no disease-free equilibrium.That is to say,the epidemic won’t disappear but will become a local disease.Further,the influence of q on the epidemic model is analyzed.更多还原