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A periodic pulse differential equation model of tumor immunotherapy is established by considering the periodic and transient behavior of infusing immune cells. Using comparison theorem and Floquet multiplier theory of the impulsive differential equation, the boundedness of the model solution, the existence and stability of the free-tumor periodic solution are given. Furthermore, the persistence of the system is analyzed. Numerical simulations are carried to confirm the main theorems. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider a class of delay difference systems with piecewise constant nonlinearity, which includes the discrete version of an artificial neural network model of two neurons described by differential equations with piecewise constant arguments. Some interesting results are obtained for the periodicity and convergence of solutions of the systems. [Copyright &y& Elsevier]