THE STOCHASTIC SI MODEL WITH RECRUITMENT AND DEATHS .1. COMPARISON WITH THE CLOSED SIS MODEL
THE STOCHASTIC SI MODEL WITH RECRUITMENT AND DEATHS .1. COMPARISON WITH THE CLOSED SIS MODEL
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DOI：
10.1016/0025-5564(93)90018-6
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发表时间：
1993-09-01
影响因子：
4.3
通讯作者：
SIMON, CP
中科院分区：
文献类型：
--
作者：
JACQUEZ, JA;SIMON, CP
我们将SI模型的随机和确定性版本与招募、背景死亡和疾病死亡进行了比较。对于随机模型，对易感人群的平均数m(X)和被感染者的平均数m(Y)以及以传染病不灭绝为条件的均值m(X)*和m(Y)*的分析表明：(1)对于确定性模型和随机模型，如果R0小于或等于-1，疾病单调死亡；(2)如果R0和Gt；1，疾病以接近(1/R0)a的概率提前死亡，其中a是引入的感染者的数量，或者m(Y)上升到一个峰值，然后缓慢死亡。对于小种群N，峰值是一个明显的极大值。如果N大于或等于100，则m(Y)中的峰值隐藏在长的、几乎稳定的平台中，并且m(Y)*接近大范围参数值的确定性流行水平。通过仿真对分析结果进行了说明。SI模型的结果受封闭的SIS模型的相应结果的激励，并与相应的结果进行比较。
We compare the stochastic and deterministic versions of an SI model with recruitment, background deaths, and deaths due to the disease. For the stochastic version, analysis of the mean number of susceptibles, m(X), and infecteds, m(Y), and of the means conditioned on nonextinction of the infection, m(X)* and m(Y)*, shows that (1) if R0 less-than-or-equal-to 1, the disease dies out monotonically for the deterministic and stochastic models, and (2) if R0 > 1, the disease dies out early with a probability close to (1/R0)a, where a is the number of infecteds introduced, or m(Y) rises to a peak and then dies out slowly. For small populations N, the peak is an obvious maximum. If N greater-than-or-equal-to 100, the peak in m(Y) is hidden in a long, nearly stationary plateau and m(Y)* is close to the deterministic endemic level for a large range of parameter values. The analytical results are illustrated with simulations. The results for the SI model are motivated by and compared with the corresponding results for the closed SIS model.