A Review on Local Asymptotic Stability Analysis for Mathematical Models of Hematopoiesis with Delay and Delay - Dependent Coefficients ( Local Asymptotic Stability Analysis for Delay Models ) Fabien

Stability analysis of mathematical models of hematopoiesis (blood cell production process), described by differential equations with delay, needs to locate eigenvalues of characteristic equations that are usually exponential polynomial functions with delay-dependent coefficients. It is then more complicated than for ordinary differential equations to determine conditions for all roots to have negative real parts. We present, on three models of increasing complexity, the tools and method that can be used, with their advantages and their limitations. The method consists in the reduction of the problem to the localization of roots of a real function, these roots giving critical values of the delay for which stability possibly switches.