Liu2017  Dynamics of Avian Influenza with Allee Growth Effect
Model Identifier
BIOMD0000000709
Short description
Format
SBML
(L2V4)
Related Publication
 Nonlinear dynamics of avian influenza epidemic models.
 Liu S, Ruan S, Zhang X
 Mathematical biosciences , 1/ 2017 , Volume 283 , pages: 118135 , 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 birdtohuman 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: Sarubini Kananathan
Modellers: Sarubini Kananathan
Submitter of this revision: Sarubini Kananathan
Modellers: Sarubini Kananathan
Metadata information
is (2 statements)
isDescribedBy (1 statement)
hasTaxon (2 statements)
hasProperty (2 statements)
isDescribedBy (1 statement)
hasTaxon (2 statements)
hasProperty (2 statements)
Mathematical Modelling Ontology
Ordinary differential equation model
Experimental Factor Ontology avian influenza
Experimental Factor Ontology avian influenza
Curation status
Curated
Modelling approach(es)
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Connected external resources
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Model files 

Liu2017  Dynamics of Avian Influenza with Allee Growth Effect.xml  SBML L2V4 representation of Liu2017  Dynamics of Avian Influenza with Allee Growth Effect  42.73 KB  Preview  Download 
Additional files 

4C_Reactions.cps  Copasi File for Figure 4c  62.81 KB  Preview  Download 
Liu2017  Dynamics of Avian Influenza with Allee Growth Effect.cps  Copasi File for Figure 4b.  75.07 KB  Preview  Download 
 Model originally submitted by : Sarubini Kananathan
 Submitted: Aug 24, 2018 4:47:22 PM
 Last Modified: Oct 8, 2018 1:28:55 PM
Revisions

Version: 7
 Submitted on: Oct 8, 2018 1:28:55 PM
 Submitted by: Sarubini Kananathan
 With comment: Automatically added model identifier BIOMD0000000709

Version: 5
 Submitted on: Aug 24, 2018 4:47:22 PM
 Submitted by: Sarubini Kananathan
 With comment: Model revised without commit message
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Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species  Initial Concentration/Amount 

S a 0000514 ; Aves 
100000.0 mol 
I h 0000511 ; Homo sapiens 
0.0 mol 
S h 0000514 ; Homo sapiens 
1000000.0 mol 
R h Recovered or Resolved ; Homo sapiens 
0.0 mol 
Reactions
Reactions  Rate  Parameters 

S_a => I_a  Avian_population*beta_a*S_a*I_a  beta_a = 1.8E8 
I_h =>  compartment*delta_h*I_h  delta_h = 0.3445 
I_h => R_h  compartment*gamma*I_h  gamma = 0.1 
S_h => I_h; I_a  beta_h*I_a*S_h  beta_h = 6.0E9 
S_h =>  compartment*mu_h*S_h  mu_h = 3.91E5 
R_h =>  compartment*mu_h*R_h  mu_h = 3.91E5 
=> S_a  Avian_population*r_a*S_a*(1S_a/M_a)*(S_a/m_a1)  m_a = 800.0; r_a = 0.005; M_a = 50000.0 
=> S_h  compartment*pi_h  pi_h = 30.0 
Curator's comment:
(added: 08 Oct 2018, 13:26:08, updated: 08 Oct 2018, 13:26:08)
(added: 08 Oct 2018, 13:26:08, updated: 08 Oct 2018, 13:26:08)
Figure 4b of the reference publication has been reproduced. Simulation of the allee effect model for avian population. Initial conditions stated in the publication did not reproduce the figures and the author was contacted for the correct values. The correct initial conditions are S_a(0)= 100000, I_a(0)= 1000, S_h(0)= 1000000, I_h(0)= 0, R_h(0)= 0, Pi_h=30 and beta_a value as per the legend. The model was simulated using Copasi 4.22 and the figure was generated using Python 2.7.