A branching process model of telomere shortening

A branching process model of a certain cell population is considered. The population is divided into types according to the number of remaining chromosome end units. This leads to a reducible multi-type Bellman-Harris branching process which turns out to exhibit polynomial growth dynamics: let be the expected number of j-type cells of age less than a at time t starting from a k-type ancestor cell. Then, as where the constant C depends on a,j and k. and can be given explicitely. The proof is fairly short and simple, using elementary results from renewal theory and a Tauberian theorem for Laplace-Stieltjes transforms