Analysis of a Dynamic Model of Host-parasite Interaction with Delay and Treatment  

作　　者：ZHO Yu 

机构地区：[1]Business School, University of Shanghai for Science and Technology, Shanghai 200093, China [2] Department of Mathemagies and Computer Science, Ningxia Teacher's College, Guyuan 756000, China

出　　处：《Chinese Quarterly Journal of Mathematics》2013年第1期118-128,共11页数学季刊（英文版）

基　　金：Foundation item： Supported by the Natural Science Foundation of Ningxia Province（NZ10228）; Supported by the Research is Funded by Ningxia Teacher＇s College Innovation Team Project（ZY201210）

摘　　要：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 R0 , 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.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 R0, which determined the betaviors 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 T as a bifurcation parameter, the infection equilibrium bifurcate a family of periodic solution as T 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.

关 键 词：stability drug treatment DELAY Hopf bifurcation periodic solution 

分 类 号：O175.1[理学—数学]