Open AccessGlobal analysis of a simple parasite-host model with homoclinic orbits
Author(s) -
Jianquan Li,
Yanni Xiao,
Yali Yang
Publication year - 2012
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2012.9.767
Subject(s) - homoclinic orbit , simple (philosophy) , host (biology) , parasite hosting , statistical physics , mathematics , biology , physics , computer science , ecology , epistemology , bifurcation , philosophy , nonlinear system , quantum mechanics , world wide web
In this paper, a simple parasite-host model proposed by Ebert et al.(2000) is reconsidered. The basic epidemiological reproduction number of parasite infection (R0) and the basic demographic reproduction number of infected hosts (R1) 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 R0 are found. The effects of R0 and R1 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 R0. In particular, it is found that full loss of fecundity of infected hosts may lead to appearance of the singular case.