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Lyapunov stability analysis of a model describing hematopoiesis

The knowledge of Lyapunov-Krasovskii functionals offers strong advantages when investigating the local or global stability properties of equilibrium points of a system with delay. Unfortunately, in many cases the construction of these functionals is not an easy task. This is the case of the model describing hematopoiesis, which is a nonlinear system with distributed delays, which, according to some conditions, admits one or two equilibrium points. By contrast with approaches already used to study this model, we analyze the stability properties of its equilibrium points by constructing Lyapunov-Krasovskii functionals of two types.