Global stability and Hopf bifurcation of a host-parasite system  

作　　者：Xuerui Wei Zhipeng Qiu 

机构地区：[1]Department of Mathematics, Nanjing University of Science and Technology Nanjing 210095, P. R. China [2]Department of Mathematics, Shaoxing University Zhejiang 312000, P. R. China

出　　处：《International Journal of Biomathematics》2017年第4期31-49,共19页生物数学学报（英文版）

摘　　要：Understanding the dynamical mechanism of the host-parasite interactions is one of important issues on host-parasite association. In this paper, we formulate a three- dimensional host macroparasite system to describe the host-parasite interactions, which includes the logistic growth rate of host population, the important free-living stage and the host fecundity reduction due to parasite infection. The purpose of the paper is to investigate the asymptotical behavior of the system. By using the properties of the solu- tion to non-autonomous linear system, the basic production number T^0 is proved to be a threshold which determines the outcome of the parasites. If TO0 〈 1, the parasite will eventually die out, and if 7-~0 〉 1 the parasite will be uniformly persistent. Hopf bifur- cation of the system is further studied, and sufficient conditions for the Hopf bifurcation are obtained. By using the singular perturbation techniques, the system is separated into two time scales with a faster time scale for the free-living infective particles and a slower time scale for the population dynamics of host and parasite, and then a complete analysis of the dynamics on the slow manifold is conducted. The theoretical results show that the level of aggregation of parasites within host may influence the persistence and stability of the system.

关 键 词：Host-parasite system THRESHOLD Hopf bifurcation stability singular pertur-bation. 

分 类 号：G[文化科学]