关键词: stability, drug treatment, delay, Hopf bifurcation, periodic solution

Abstract: In this paper, the dynamic behaviors of a host-parasite model with intracellular delay and drug treatment is investigated. we obtain the basic reproductive ratio R_0, which determined the behaviors of the system. If R₀<1, the infection-free equilibrium is globally asymptotic stability. If 1<R₀<3, the infection equilibrium is locally asymptotic stability. If R₀>3, by choosing the delay τ as a bifurcation parameter, the infection equilibrium bifurcate a family of periodic solution as τ crosses a critical value. Furthermore, we give some examples to verify our theoretical results and discuss the sensitivity of the drug efficacy and effect of the delay. In the finally, we give a brief discussion.

Key words: stability, drug treatment, delay, Hopf bifurcation, periodic solution