On the Final Size of Epidemics with Seasonality
On the Final Size of Epidemics with Seasonality
复制标题
DOI：
10.1007/s11538-009-9433-7
复制
发表时间：
2009-11-01
影响因子：
3.5
通讯作者：
Gomes, M. Gabriela M.
中科院分区：
文献类型：
--
作者：
Bacaer, Nicolas;Gomes, M. Gabriela M.
我们首先研究了一个描述季节性环境中流行病的具有周期系数的SIR微分方程组。与恒定环境不同，最终的流行规模可能不是基本繁殖数R-0或感染者初始比例的增函数。此外，即使R-0 < 1，也可能发生大规模流行病。但就像在一个恒定的环境中，当R-0 1时，最终的流行病规模趋于0< 1 and the initial fraction of infected people tends to 0. When R-0 >，最终的流行病规模大于初始非免疫群体的分数1-1/R-0。总之，基本再生数R-0保持其经典的阈值性质，但许多其他性质在季节性环境中不再成立。在分析新出现的病媒传播疾病（西尼罗河、登革热、基孔肯雅热）或空气传播疾病（SARS、大流行性流感）的数据时，应牢记这些理论结果;所有这些疾病都受到季节性的影响。
We first study an SIR system of differential equations with periodic coefficients describing an epidemic in a seasonal environment. Unlike in a constant environment, the final epidemic size may not be an increasing function of the basic reproduction number R-0 or of the initial fraction of infected people. Moreover, large epidemics can happen even if R-0 < 1. But like in a constant environment, the final epidemic size tends to 0 when R-0 < 1 and the initial fraction of infected people tends to 0. When R-0 > 1, the final epidemic size is bigger than the fraction 1-1/R-0 of the initially nonimmune population. In summary, the basic reproduction number R-0 keeps its classical threshold property but many other properties are no longer true in a seasonal environment. These theoretical results should be kept in mind when analyzing data for emerging vector-borne diseases (West-Nile, dengue, chikungunya) or air-borne diseases (SARS, pandemic influenza); all these diseases being influenced by seasonality.