A ratio-dependent impulsive control of an SIQS epidemic model with non-linear incidence

Abstract

In this paper, the ratio-dependent impulsive control is used in an SIQS epidemic model with non-linear incidence. Compared with most of existing results, there are two advantages. On the one hand, the impulsive control strategy is economical, efficient and simple. On the other hand, the ratio-dependent impulsive control can deal with the changing population well. Besides, by using analogue of the Poincare criterion, vector field analysis, Poincare map and the method of qualitative analysis, the stability of the disease-free equilibrium and the existence and stability of positive order-k periodic solution of the SIQS epidemic model under ratio-dependent impulsive control are studied. Moreover, our results show that order-k (k>2) periodic solutions don’t exist. Finally, some simple numerical examples are used to verify our theoretical results.