Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 444, Issue 2, Pages 1542-1564Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2016.07.027
Keywords
HIV-1 model; Cell-to-cell transmission; Spatial heterogeneity; Global asymptotic stability; Lyapunov functions; Basic reproduction number
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Funding
- National Natural Science Foundation of China [11401182, 11471089]
- Science and Technology Innovation Team in Higher Education Institutions of Heilongjiang Province [2014TD005]
- Youth Innovation Talents of Department of Education, Heilongjiang Province
- Japan Society for the Promotion of Science [15K17585]
- program of the Japan Initiative for Global Research Network on Infectious Diseases (J-GRID)
- Japan Agency for Medical Research and Development, AMED
- Grants-in-Aid for Scientific Research [15K17585] Funding Source: KAKEN
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This paper is concerned with the global dynamics of a PDE viral infection model with cell-to-cell transmission and spatial heterogeneity. The basic reproduction number R-0, which is a threshold value that predicts whether the infection will go to extinction or not, is defined in a variational characterization. In quite a general setting in which every parameter can be spatially heterogeneous, it is shown that if R-0 <= 1, then the infection-free steady state is globally asymptotically stable, while if R-0 > 1, then the system is uniformly persistent and the infection steady state is globally asymptotically stable. The proof is based on the construction of the Lyapunov functions and usage of the Green's first identity. Finally, numerical simulation is performed in order to verify the validity of our theoretical results. (C) 2016 Elsevier Inc. All rights reserved.
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