Influence of latent period and nonlinearincidence rate on the dynamics of SIRS epidemiological models
Influence of latent period and nonlinearincidence rate on the dynamics of SIRS epidemiological models
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DOI：
10.3934/dcdsb.2010.13.195
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发表时间：
2009-10
影响因子：
1.2
通讯作者：
Yu Yang;Dongmei Xiao
中科院分区：
文献类型：
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作者：
Yu Yang;Dongmei Xiao
考虑具有潜伏期和非线性发病率的SIRS型疾病传播模型。潜伏期设为常数$\tau$，发病率设为特定的非线性形式$\frac{kI(t-\tau)S(t)}{1+\alpha I^{h}(t-\tau)}$，其中$h\ge 1$。研究了该模型的无病平衡点的稳定性和地方性平衡点的存在性、唯一性和稳定性。结果表明，存在与非线性发病率形式无关的基本繁殖数$R_0$，如果$R_0\le 1$，则无病平衡点是全局渐近稳定的；如果$R_0>1$，则在无潜伏期的模型可行区域内，唯一的地方病平衡点是全局渐近稳定的。周期解可以由Hopf分岔从模型在临界潜伏期的地方性平衡中得到。给出了一些数值模拟来支持我们的分析结论。
A disease transmission model of SIRS type with latent period and nonlinear incidence rate is considered. Latent period is assumed to be a constant $\tau$, and the incidence rate is assumed to be of a specific nonlinear form, namely, $\frac{kI(t-\tau)S(t)}{1+\alpha I^{h}(t-\tau)}$, where $h\ge 1$. Stability of the disease-free equilibrium, and existence, uniqueness and stability of an endemic equilibrium for the model, are investigated. It is shown that, there exists the basic reproduction number $R_0$ which is independent of the form of the nonlinear incidence rate, if $R_0\le 1$, then the disease-free equilibrium is globally asymptotically stable, whereas if $R_0>1$, then the unique endemic equilibrium is globally asymptotically stable in the interior of the feasible region for the model in which there is no latency, and periodic solutions can arise by Hopf bifurcation from the endemic equilibrium for the model at a critical latency. Some numerical simulations are provided to support our analytical conclusions.