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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 HIV infection model with CTL-response delay and analyze the effect of time delay on stability of equilibria. We obtain the global stability of the infection-free equilibrium and give sufficient conditions for the local stability of the CTL-absent equilibrium and CTL-present equilibrium. By choosing the CTL-response delay as a bifurcation parameter, we prove that the CTL-present equilibrium is locally asymptotically stable in a range of delays and a Hopf bifurcation occurs as crosses a critical value. Numerical simulations are given to support the theoretical results. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a tri-neuron network model with discrete and distributed delays. After discussing the distributions of the roots of the characteristic equation local stability analysis of the steady-state solution leads to, we analyze the stability of network models with instantaneous feedback and neural interaction history, delayed neural feedback and no neural interaction history and delayed neural feedback and neural interaction history; we give sufficient conditions for the linear stability of the equilibrium solution; we also show that a Hopf bifurcation can occur when the delays take certain critical values; and we further prove that there is a positive integer K such that there are K switches from stability to instability and back to stability. Numerical simulations are finally performed to illustrate the obtained results. [Copyright &y& Elsevier]