一类具有不同传染力的SEI_1I_2R传染病模型

A Type of SEI_1I_2R Epidemic Model with Different Infectiousness

本文提出并研究了带有人口迁入、具有不同传染力的SEI_1I_2R传染病模型,传染率βSI/(H+I)为非线性,通过构建再生矩阵求出基本再生数R_0,得到相关模型的无病平衡点与地方病平衡点稳定性的充分条件.当R_0<1时,无病平衡点P_0在■内全局渐近稳定,疾病最终消亡;当R_0>1时,地方病平衡点P~*是局部渐近稳定的,即传染病会持续存在.

A type of SEI1I2R epidemic models with different infectiousness along with the population migration is proposed and studied in this paper. The rate βSI/(H+I) of such an infection presents nonlinearity. The basic reproductive rate R0 is determined by constructing the regeneration matrix and therefore the sufficient conditions for the stability of the disease free equilibrium and endemic equilibrium of correlation models are obtained. It is shown that the disease free equilibrium P0 within Γ is globally asymptotically stable and the disease ultimately dies out if R0<1, while the endemic equilibrium point P* is locally asymptotically stable if R0>1, ie. the infectious diseases will continuously exist.