一类具有饱和发生率和环境感染的传染病模型的稳定性

Stability of epidemic model with saturation incidence and environmental infection

讨论一类具有饱和发生率和环境感染的传染病模型的稳定性.利用下一代矩阵法得到了基本再生数R0的表达式.当R0<1时,通过构造Lyapunov函数并利用LaSalle不变集原理,证明了模型在无病平衡点处全局渐近稳定;当R0>1时,证明了地方病平衡点存在且唯一.最后,通过数值模拟验证无病平衡点的稳定性,并分析疫苗接种率对基本再生数的影响.

The stability of a epidemic model with saturation incidence and environmental infection is discussed.The expression of basic reproduction number R0 is obtained by using the next-generation matrix method.When R0<1,the global asymptotic stability of the system at the disease-free equilibrium is proved by constructing Lyapunov function and using LaSalle′s invariance principle.When R0>1,it is proved that the system exists a unique endemic equilibrium.Finally,the stability of disease-free equilibriummain is verified and the effect of vaccination rate on the basic reproduction number is analyzed by numerical simulation.