Large fluctuations in multi-scale modeling for rest hematopoiesis

Hematopoiesis is a biological phenomenon (process) of production mature blood cells by cellular differentiation. It based on amplification steps due to an interplay between renewal and differentiation in the successive cell types from stem cells. We will study this mechanism with stochastic point view explain unexpected fluctuations number, as surprisingly observed biologists medical doctors rest hematopoiesis. consider three types: cells, progenitors Each type characterized its own dynamics parameters, division rate probabilities at each event. model global population three-dimensional decomposable branching process. show that given inverse small difference probabilities. Introducing parameter K which scales simultaneously size first component, death rate, we describe asymptotic behavior process for large K. has time scales. Focusing third prove size, conveniently renormalized (in size), expanded unusual way inducing fluctuations. The proofs are fine different involved use convergence average techniques proofs.