Global analysis of a simple parasite-host model withhomoclinic orbits - Jianquan Li; Yanni Xiao; Yali Yang (Mathematical Biosciences and Engineering)
In this paper, a simple parasite-host model proposed by Ebert etal.(2000) is reconsidered. The basic epidemiological reproductionnumber of parasite infection ($R_0$) and the basic demographicreproduction number of infected hosts ($R_1$) are given. The globaldynamics of the model is completely investigated, and the existenceof heteroclinic and homoclinic orbits is theoretically proved,which implies that the outbreak of parasite infection may happen.The thresholds determining the host extinction in the presence ofparasite infection and variation in the equilibrium level of theinfected hosts with $R_0$ are found. The effects of $R_0$ and $R_1$on dynamics of the model are considered and we show that theequilibrium level of the infected host may not be monotone withrespect to $R_0$. In particular, it is found that full loss offecundity of infected hosts may lead to appearance of the singularcase.