Growth rate and basic reproduction number for population models with a simple periodic factor
Growth rate and basic reproduction number for population models with a simple periodic factor
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DOI：
10.1016/j.mbs.2007.07.005
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发表时间：
2007-12-01
影响因子：
4.3
通讯作者：
Ouifki, Rachid
中科院分区：
文献类型：
--
作者：
Bacaer, Nicolas;Ouifki, Rachid
对于具有正弦周期因子的连续时间种群模型，增长率和基本再生数都被证明是涉及连分数的简单方程的最大根。作为一个例子，我们重新考虑了 Williams 和 Dye 研究的具有固定潜伏期、指数分布感染期和正弦接触率的 SEIS 模型 [B.G. Williams，C. Dye，传播季节性变化时的传染病持续性，数学。生物科学。 145（1997）77]。我们表明，除了一些特殊的参数值外，流行病阈值不仅取决于平均接触率，还取决于波动幅度。 (C) 2007 Elsevier Inc. 保留所有权利。
For continuous-time population models with a periodic factor which is sinusoidal, both the growth rate and the basic reproduction number are shown to be the largest roots of simple equations involving continued fractions. As an example, we reconsider an SEIS model with a fixed latent period, an exponentially distributed infectious period and a sinusoidal contact rate studied in Williams and Dye [B.G. Williams, C. Dye, Infectious disease persistence when transmission varies seasonally, Math. Biosci. 145 (1997) 77]. We show that apart from a few exceptional parameter values, the epidemic threshold depends not only on the mean contact rate, but also on the amplitude of fluctuations. (C) 2007 Elsevier Inc. All rights reserved.