Affiliation:
1. School of Science, Xi’an University of Technology, Xi’an 710048, P. R. China
Abstract
In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number [Formula: see text] and the relation of the endemic equilibrium [Formula: see text] and the ratio threshold [Formula: see text], dynamical analysis of the controlled system is conducted. Under the control strategy, if [Formula: see text], the solutions converge to the disease-free equilibrium. If [Formula: see text] and [Formula: see text], the impulsive system has periodic solution that is orbitally asymptotically stable, and order-[Formula: see text] periodic solution does not exist. Furthermore, if [Formula: see text] and [Formula: see text], the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results.
Funder
National Natural Science Foundation of China
Scientific Research Program Project of Education Department of Shaanxi Province, China
Natural Science Basic Research Plan in Shaanxi Province of China
Publisher
World Scientific Pub Co Pte Ltd