期刊
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
卷 458, 期 2, 页码 1115-1130出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2017.09.045
关键词
Attraction basin; Bacteria-infective population model; Delayed reaction-diffusion equation
资金
- National Natural Science Foundation of China [11571371, 71471020]
- Hunan Provincial Natural Science Foundation [2016JJ1001]
- Scientific Research Fund of Hunan Provincial Education Department [15A003]
- China Postdoctoral Science Foundation [2014M550097, 2015T80144]
This paper considers a class of delayed reaction-diffusion systems under the Neumann boundary condition which arise in epidemiology and can describe the temporal and spatial evolutionary phenomena for the bacteria population and the human infective population. With the help of the iterative properties of interval mapping and dynamical system approaches, some positively invariant sets and attractive basins of the considered systems are analyzed detailedly. In addition, combining the global attractivity of interval mapping, we provide some sufficient conditions to ensure local or global attractivity of steady states of the systems. Finally, we apply these theoretical results to some models with different nonlinearity demonstrating force of infection, and then obtain some sufficient conditions about force of infection to describe the survival and extinction of bacteria and infective populations. (C) 2017 Elsevier Inc. All rights reserved.
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