In this paper, our interest is in the perturbation analysis of level‐dependent quasi‐birth‐and‐death (LD‐QBD) processes, which constitute a wide class of structured Markov chains. An LD‐QBD process has the special feature that its space of states can be structured by levels (groups of states), so that a tridiagonal‐by‐blocks structure is obtained for its infinitesimal generator. For these processes, a number of algorithmic procedures exist in the literature in order to compute several performance measures while exploiting the underlying matrix structure; among others, these measures are related to first‐passage times to a certain level L(0) and hitting probabilities at this level, the maximum level visited by the process before reaching states of level L(0), and the stationary distribution. For the case of a finite number of states, our aim here is to develop analogous algorithms to the ones analyzing these measures, for their perturbation analysis. This approach uses matrix calculus and exploits the specific structure of the infinitesimal generator, which allows us to obtain additional information during the perturbation analysis of the LD‐QBD process by dealing with specific matrices carrying probabilistic insights of the dynamics of the process. We illustrate the approach by means of applying multitype versions of the susceptible‐infective (SI) and susceptible‐infective‐susceptible (SIS) epidemic models to the spread of antibiotic‐sensitive and antibiotic‐resistant bacterial strains in a hospital ward.

中文翻译：

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有限 LD-QBD 过程中的扰动分析及其在流行病模型中的应用。

在本文中，我们的兴趣是对水平相关的准生死（LD-QBD）过程的扰动分析，该过程构成了一类广泛的结构化马尔可夫链。LD-QBD过程的一个特点是它的状态空间可以通过级别（状态组）来构造，从而为其无穷小的生成器获得三对角块结构。对于这些过程，文献中存在许多算法程序，以便在利用底层矩阵结构的同时计算多种性能指标；其中，这些度量与到达某个级别L (0) 的首次通过时间和该级别的命中概率、在达到级别L (0)状态之前过程访问的最大级别以及平稳分布有关。对于有限数量状态的情况，我们的目标是开发与分析这些测量的算法类似的算法，以进行扰动分析。这种方法使用矩阵微积分并利用无穷小生成器的特定结构，这使我们能够在 LD-QBD 过程的扰动分析过程中通过处理带有过程动力学概率见解的特定矩阵来获得附加信息。我们通过将易感-感染（SI）和易感-感染-易感（SIS）流行病模型的多种版本应用于医院病房中抗生素敏感和抗生素耐药菌株的传播来说明该方法。