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Global analysis of a simple parasite-host model with homoclinic orbits

1. Faculty of Science, Air Force Engineering University, Xi'an 710051
2. Department of Applied Mathematics, Xi'an Jiaotong University, Xi'an 710049

In this paper, a simple parasite-host model proposed by Ebert et al.(2000) is reconsidered. The basic epidemiological reproduction number of parasite infection ($R_0$) and the basic demographic reproduction number of infected hosts ($R_1$) are given. The global dynamics of the model is completely investigated, and the existence of 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 of parasite infection and variation in the equilibrium level of the infected 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 the equilibrium level of the infected host may not be monotone with respect to $R_0$. In particular, it is found that full loss of fecundity of infected hosts may lead to appearance of the singular case.
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Keywords homoclinic orbit; Parasite-host model; global dynamics; reproduction number.

Citation: Jianquan Li, Yanni Xiao, Yali Yang. Global analysis of a simple parasite-host model with homoclinic orbits. Mathematical Biosciences and Engineering, 2012, 9(4): 767-784. doi: 10.3934/mbe.2012.9.767

 

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