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Introduction. Drug resistance is a very serious problem not least for chemotheaputic treatment of cancer and it is very important to understand, as far as possible, ways to countermeasure drug resistance in a number of biomedical contexts . In order to unravel the possible mechanisms responsible for this phenomena Iwasa and coworkers developed a prominent theoretical model of the evolutionary dynamics of escape[1, 2]. They base their approach on the assumption that n point mutations in some crucial parts of the genome are necessary for escape. They further assumed that the different mutants can be described by binary strings (with entries +1 or − 1) of length n . There are 2 n − 1 such mutants. It is assumed that treatment reduces the proliferation ratios of sensitive mutants: R < 1 whereas resistant mutants are such that R > 1. The corresponding evolutionary dynamics is modelled in terms of Galton-Watson multitype branching process (GWMBP) [3] where at each generation each individual of each type has a given (in general, mutant-dependent) probability of mutating and producing offspring belonging to a different type. The problem is to calculate the probability that a resistant mutant is reached within a population of size N . The model proposed by Iwasa et al. has been analysed in more detail in [4, 5]. Whilst this approach is both biologically and mathematically sound, we believe the efficiency with which evolutionary escape allows organisms to avoid extinction, when attacked by lethal 

