网络上具有一般直接免疫的SIRS传染病模型分析

An Analysis of an SIRS Epidemic Model with General Direct Immunization in Networks

考虑复杂网络上具有一般直接免疫率的SIRS传染病模型。由地方病平衡点的存在性,确定了传染病的流行阈值λc,并且通过构造合适的李雅普诺夫函数证明:当λ≤λ_c时,无病平衡点全局渐近稳定;当λ>λ_c时,地方病平衡点全局渐近稳定。根据免疫率的分布,提出了一致性直接免疫和目标性直接免疫。结果表明,在平均免疫率相等的条件下存在免疫丧失率的临界值δ_c,当δ<δ_c(δ>δ_c)时,目标性免疫的流行阈值小于(大于)一致性免疫的流行阈值。

We consider an SIRS epidemic model with a general direct immunization rate on networks.By constructing suitable Lyapunov functions,we find that the dynamical behvaior of the model is completely determined by the epidemic thresholdλc.Whenλ≤λ_c,the disease-free equilibrium is globally asymptotically stable;whenλ>λ_c,the endemic equilibrium is globally asymptotically stable.In addition,we propose a uniform direct immunization and a targeted direct immunization.The results show that under the same average immunization rate s there exists a critical immunization-lost rateδcso that the epidemic threshold of the targeted direct immunization is smaller(larger)than that of the uniform direct immunization if δ<δ_c(δ>δ_c).