Global behavior of a host-parasitoid model under the constant refuge effect

In this paper, we discuss the qualitative behavior of a modified host-parasitoid model in which there is a constant number of hosts in a refuge, i.e., the fixed number of hosts are safe from attack by parasitoid. More precisely, we study the boundedness and persistence, existence and uniqueness of positive equilibrium point, local asymptotic stability and global behavior of unique positive equilibrium point, and the rate of convergence of the solutions that converge to the unique positive equilibrium point of the modified host-parasitoid model. Some numerical examples are given to verify our theoretical results.