Persistence and periodicity of survival red blood cells model with time-varying delays and impulses

In this paper, a class of survival red blood cells model with time-varying delays and impulsive effects is considered. First, some sufficient conditions for the persistence are derived by use of the theory on impulsive differential equations. The persistence describes the persistent survival of the mature red blood cells in the mammal under delay and impulsive perturbations. Then assuming that the coefficients in the model are $\omega$-periodic, some criteria ensuring the existence-uniqueness and global attractivity of positive $\omega$-periodic solution of the addressed model are obtained, which are suitable for survival red blood cells model with any $\omega \in {\mathbb{R}}_{+}$. These global attractivity criteria describe the nonexistence of any dynamic diseases in the mammal. Moreover, our proposed results in this paper extend and improve some recent works in the literature. Finally, two examples and their computer simulations are given to show the effectiveness and advantages of the results.