Existence of order-1 periodic solutions for a viral infection model with state-dependent impulsive control - Huilan Wang; Binxiang Dai; Qizhen Xiao (Advances in Difference Equations, 2019)
Abstract It is well known that the drug treatment is always combined with the injection of immune factors. In this paper, a virus infection model with state-dependent impulsive control is considered. Firstly, by deriving three categories of Bendixson domain and using the methods of geometry and successor function, we establish some criteria for the existence of positive order-1 periodic solution for a general model, which extends the existing results in the literature. Further, the criteria are used to obtain the existence of positive order-1 periodic solutions in the two cases that the positive equilibrium point is on the left or right side of the pulse line, respectively. Finally, an example is presented to illustrate our results.