Control theoretic approach to analysis of random branching walk models arising in molecular biology

We present two models of molecular processes described by infinite systems of first order differential equations. These models result from branching random walk processes used to represent the evolution of particles in these problems. Using asymptotic techniques based on Laplace transforms it is possible to characterize the asymptotic behavior of telomeres shortening which is supposed to be the mechanism of aging and evolution of cancer cells with increasing number of copies genes responsible for coding causing drug removal or metabolisation. The analysis in both cases is possible because they could be represented by systems with positive feedbacks.