Model Identifier
BIOMD0000000708
Short description
Sanhong Liu, Shigui Ruan & Xinan Zhang. Nonlinear dynamics of avian influenza epidemic models. Mathematical Biosciences 283 (2017).
Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior. We obtain a threshold value for the prevalence of avian influenza and investigate the local or global asymptotical stability of each equilibrium of these systems by using linear analysis technique or combining Liapunov function method and LaSalle's invariance principle, respectively. Moreover, we give necessary and sufficient conditions for the occurrence of periodic solutions in the avian influenza system with Allee effect of the avian population. Numerical simulations are also presented to illustrate the theoretical results.
Format
SBML
(L2V4)
Related Publication
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Nonlinear dynamics of avian influenza epidemic models.
- Sanhong Liu, Shigui Ruan, Xinan Zhang
- Mathematical biosciences , 1/ 2017 , Volume 283 , pages: 118-135 , PubMed ID: 27887851
- School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, 437100, China; School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China.
- Avian influenza is a zoonotic disease caused by the transmission of the avian influenza A virus, such as H5N1 and H7N9, from birds to humans. The avian influenza A H5N1 virus has caused more than 500 human infections worldwide with nearly a 60% death rate since it was first reported in Hong Kong in 1997. The four outbreaks of the avian influenza A H7N9 in China from March 2013 to June 2016 have resulted in 580 human cases including 202 deaths with a death rate of nearly 35%. In this paper, we construct two avian influenza bird-to-human transmission models with different growth laws of the avian population, one with logistic growth and the other with Allee effect, and analyze their dynamical behavior. We obtain a threshold value for the prevalence of avian influenza and investigate the local or global asymptotical stability of each equilibrium of these systems by using linear analysis technique or combining Liapunov function method and LaSalle's invariance principle, respectively. Moreover, we give necessary and sufficient conditions for the occurrence of periodic solutions in the avian influenza system with Allee effect of the avian population. Numerical simulations are also presented to illustrate the theoretical results.
Contributors
Submitter of the first revision: Sarubini Kananathan
Submitter of this revision: Lucian Smith
Curator: Lucian Smith
Modeller: Sarubini Kananathan
Submitter of this revision: Lucian Smith
Curator: Lucian Smith
Modeller: Sarubini Kananathan
Metadata information
is (2 statements)
isDescribedBy (2 statements)
hasTaxon (2 statements)
hasProperty (2 statements)
isDescribedBy (2 statements)
hasTaxon (2 statements)
hasProperty (2 statements)
Experimental Factor Ontology
avian influenza
Mathematical Modelling Ontology Ordinary differential equation model
Mathematical Modelling Ontology Ordinary differential equation model
Curation status
Curated
Modelling approach(es)
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