This paper investigates a population model which grows as per the Markovian arrival process and is influenced by binomial catastrophes that occur according to renewal process. That is, when a catastrophe attacks, an individual (element) of the population survives with probability p or dies with probability \(1-p\), independent of anything else. Using the supplementary variable technique, the steady-state vector generating function (VGF) of the population size distribution at post-catastrophe epoch is obtained in terms of the infinite product of matrices. Further, the VGF of the population size distribution at arbitrary and pre-catastrophe epochs are also deduced. To make the model valuable for practitioners, a step-wise computing process for evaluation of the distribution of population size at various epochs is given. A recursive formula to compute factorial moments of the population size is also presented. Finally, some numerical results are included to illustrate the impact of parameters on the behavior of the model.

本文研究了一个根据马尔可夫到达过程增长并受到根据更新过程发生的二项式灾难影响的人口模型。也就是说，当灾难来袭时，种群中的个体（元素）以概率p生存或以概率\(1-p\)死亡，独立于其他任何东西。使用补充变量技术，根据矩阵的无限乘积获得灾后时期人口规模分布的稳态向量生成函数（VGF）。此外，还推导出了任意和灾前时期人口规模分布的 VGF。为了使模型对从业者有价值，给出了一个逐步计算过程，用于评估各个时期的人口规模分布。还提出了一个计算种群规模阶乘矩的递归公式。最后，包括一些数值结果来说明参数对模型行为的影响。