[1] Wang Yaping, Chen Wenyan,. Existence for positive steady states of an eco-epidemiological model [J]. Journal of Southeast University (English Edition), 2011, 27 (1): 119-122. [doi:10.3969/j.issn.1003-7985.2011.01.025]

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Existence for positive steady states of an eco-epidemiological model()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

27

Issue:

2011 1

Page:

119-122

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2011-03-30

Info

Title:

Existence for positive steady states of an eco-epidemiological model

Author(s):

Wang Yaping;  Chen Wenyan

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

eco-epidemiological model;  existence;  positive steady states

PACS:

O175.25

DOI:

10.3969/j.issn.1003-7985.2011.01.025

Abstract:

An eco-epidemiological model with an epidemic in the predator and with a Holling type Ⅱ function is considered. A system with diffusion under the homogeneous Neumann boundary condition is studied. The existence for a positive solution of the corresponding steady state problem is mainly discussed. First, a prior estimates(positive upper and lower bounds)of the positive steady states of the reaction-diffusion system is given by the maximum principle and the Harnack inequation. Then, the non-existence of non-constant positive steady states by using the energy method is given. Finally, the existence of non-constant positive steady states is obtained by using the topological degree.

References:

[1] Guo Z K, Li W L, Cheng L H, et al. Eco-epidemiological model with epidemic and response function in the predator[J]. Journal of Lanzhou University: Natural Sciences, 2009, 45(3):117-121.(in Chinese)
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[8] Chen W Y, Wang M X. Non-constant positive steady-states of a predator-prey-mutualist model[J]. Chin Ann Math: Series B , 2004, 25(2):243-254.
[9] Lin C S, Ni W M, Takagi I. Large amplitude stationary solutions to a chemotaxis system [J].Differential Equations, 1988, 72:1-27.
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[11] Wu Z Q, Yi J X, Wang C P. An introduction to elliptic and parabolic equations [M].Beijing: Science Press, 2003.(in Chinese)
[12] Pang P Y H, Wang M X, Qualitative analysis of a ratio-dependent predator-prey system with diffusion[J]. Proc Roy Soc Edinburgh A, 2003, 133(4):919-942.

Memo

Memo:

Biographies: Wang Yaping(1986—), female, graduate; Chen Wenyan(corresponding author), female, doctor, associate professor, cwyseu@163.com.
Foundation item: The National Natural Science Foundation of China(No.10601011).
Citation: Wang Yaping, Chen Wenyan. Existence for positive steady states of an eco-epidemiological model[J].Journal of Southeast University(English Edition), 2011, 27(1):119-122.[doi:10.3969/j.issn.1003-7985.2011.01.025]

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