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In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function approach, we study two versions of such population models when the binomial catastrophic events are of a slightly different random nature. In both cases, we describe the subtle balance between the two birth and death conflicting effects.

A generating function approach to Markov chains undergoing binomial catastrophes