具有非单调发生率的SIR传染病模型的稳定性

摘要

An epidemic SIR model with nonmonotone incidence rate is considered. Firstly, the positivity, uniform boundedness and global attractivity of the solutions of systems are given. What’s more, by using the Hurwitz-Rouché criterion, the paper discusses the locally asymptotical stability of the disease-free equilibrium and the endemic equilibrium. Consequently, by upper and lower solutions method and the comparison principle, the results show that the constant input rate is big enough, the endemic equilibrium is globally asymptotically stable, the constant input rate or the contact rate is small enough, and the disease-free equilibrium is globally asymptotically stable.%研究了一类具有非单调发生率的SIR传染病模型。给出了系统解的正性、一致有界性和全局吸引性，接着运用Hurwitz-Rouché判别法，讨论了对应系统无病平衡态和地方病平衡态的局部渐近稳定性。最后通过上下解方法和比较原理说明，当常数输入率足够大时，地方病平衡态是全局渐近稳定的；当常数输入率或者接触率足够小时，无病平衡态是全局渐近稳定的。