Qualitative Analysis for Barbour's Schistosomiasis Model with Diffusion

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QI Long-xing(School of Mathematical Sciences, Anhui University, Hefei Anhui 230601 China)
CUI Jing-an(College of Science, Beijing University of Civil Engineering and Architecture, Beijing 100044 China)
Journal Title:
Journal of Biomathematics
Volume 27, Issue 01, 2012
Key Word:
Schistosomiasis model;Diffusion;Stability;Uniform upper bound;Non-constant positive steady states

Abstract´╝Ü This paper is concerned with the Barbour's schistosomiasis models which is obtained by ordinary and partial differential equations.The partial differential system is a reaction diffusion system reflecting the spatial and time distribution.The qualitative mathematical properties are analyzed in two systems.The uniform upper bound of the solutions is established by the method of the comparison principle.And applying the energy method we can show the non-existence of non-constant positive steady-state solution of the elliptic system for certain range of diffusion coefficients.

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