Lounes R, de Arazoza H
Université Paris V, Laboratoire de Statistique Médicale, UA CNRS 1323, France.
IMA J Math Appl Med Biol. 1999 Jun;16(2):143-54.
We study deterministic and stochastic versions of a birth and death process for a two-type population with immigration for both types. For the stochastic model we consider the case where the rates are time dependent, and also when they are constant, as is the case in our AIDS application. We derive the probability generating function of the bivariate process and the expectations of the marginal processes. We also study the marginal behaviour of the bivariate process in a particular case where we suppose that the first event is an immigration, and examine the behaviour of the marginal processes divided by their expectations. Finally, we apply some of these results to a sexual-partner notification system, as in the Cuban national programme on HIV/AIDS.
我们研究了具有两类移民的两类种群生死过程的确定性和随机版本。对于随机模型，我们考虑了速率随时间变化的情况，以及速率为常数的情况，就像我们在艾滋病应用中那样。我们推导了二元过程的概率生成函数以及边际过程的期望。我们还研究了在假设第一个事件是移民的特定情况下二元过程的边际行为，并考察了边际过程除以其期望后的行为。最后，我们将其中一些结果应用于性伴侣通报系统，就像古巴国家艾滋病毒/艾滋病项目那样。
