一类SI_1I_2R_1R_2传染病模型的平衡解的稳定性

Stability of a Type of SI_1I_2R_1R_2 Epidemic Model

考虑一类SI1I2R1R2传染病动力学模型,即一类对于不同种群具有不同传染率,且在治愈后具有不同抵抗力的模型;或者说是对于一种疾病在两种种群中交差感染和不同恢复率的模型.给出了疾病存在消失的阈值R0.当R0<1时,无病平衡解是全局稳定的,即疾病最终会消失;当R0>1时,存在唯一正平衡解,且在一定条件下局部稳定.最后对该文做了一些讨论.

This paper studies a type of SI1I2R1R2 epidemic model that ineorporates two classes of infectious individuals with differential infectivity and differential resistance, or in other words, an epidemic model of two competitive species with inter-infection and differential recovery. The control number Ro is found. If R0 〈 1,the disease-free equilibrium is globally asymptotical stable, and the disease always dies out in the end. If R0 〉 1, a unique endemic equilibrium is locally asymptotical stable under a special condition.