Mackey–Glass model of hematopoiesis with non-monotone feedback: Stability, oscillation and control

For the blood cell production model with a unimodal (hump) feedback functiondydt=-γy(t)+βθny(t-τ)θn+yn(t-τ),we review the known results and investigate generalizations of this equation. Permanence, oscillation and stability of the positive equilibrium are studied for non-autonomous equations, including equations with a distributed delay. In addition, a linear control is introduced, and possibilities to stabilize an otherwise unstable positive equilibrium are explored.