Journal
MATHEMATICAL BIOSCIENCES AND ENGINEERING
Volume 11, Issue 6, Pages 1295-1317Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/mbe.2014.11.1295
Keywords
Epidemic models; complex networks; demographics; basic reproduction number; global stability
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Funding
- National Sciences Foundation of China [11331009, 11171314, 11147015]
- Program for the Outstanding Innovative Teams of Higher Learning Institutions of Shanxi [2010-074]
- Research Project Supported by Shanxi Scholarship Council of China [2013-3]
- Technology Projects of Overseas Researchers in Shanxi Province (Preferential Subsidization)
- Natural Science and Engineering Research Council of Canada
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In this paper, we propose and study network epidemic models with demographics for disease transmission. We obtain the formula of the basic reproduction number Ro of infection for an SIS model with births or recruitment and death rate. We prove that if R-0 <= 1, infection-free equilibrium of SIS model is globally asymptotically stable; if R-0 > 1, there exists a unique endemic equilibrium which is globally asymptotically stable. It is also found that demographics has great effect on basic reproduction number R-0. Furthermore, the degree distribution of population varies with time before it reaches the stationary state.
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