In the garden of branching processes
In the garden of branching processes
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DOI：
10.1137/s0036144502417843
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发表时间：
2004-06-01
期刊：
影响因子：
10.2
通讯作者：
Lange, K
中科院分区：
文献类型：
--
作者：
Dorman, KS;Sinsheimer, JS;Lange, K
本文综述和发展了连续时间马氏多型分枝过程的数值方法。特别注意的是，在移民粒子的泊松流的存在下的平均值，方差，灭绝概率和边际分布的计算。泊松过程假设允许时间上复杂的移民模式，便于应用显着的泊松过程和坎贝尔公式。推导出的方法和公式适用于四个模型：两个人口遗传学模型，一个模型接种疫苗对传染病在社区的家庭，和一个模型的耐药HIV病毒在接受药物治疗的患者的增长。
The current paper surveys and develops numerical methods for Markovian multitype branching processes in continuous time. Particular attention is paid to the calculation of means, variances, extinction probabilities, and marginal distributions in the presence of a Poisson stream of immigrant particles. The Poisson process assumption allows for temporally complex patterns of immigration and facilitates application of marked Poisson processes and Campbell's formulas. The methods and formulas derived are applied to four models: two population genetics models, a model for vaccination against an infectious disease in a community of households, and a model for the growth of resistant HIV virus in patients undergoing drug therapy.