Liu2017  Dynamics of Avian Influenza with Logistic Growth
Model Identifier
BIOMD0000000708
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)
Tags
Connected external resources
Name  Description  Size  Actions 

Model files 

Liu2017  Dynamics of Avian Influenza with Logistic Growth.xml  SBML L2V4 representation of Liu2017  Dynamics of Avian Influenza with Logistic Growth  46.33 KB  Preview  Download 
Additional files 

Liu2017  Dynamics of Avian Influenza with Logistic Growth.cps  Copasi file for the model  69.77 KB  Preview  Download 
 Model originally submitted by : Sarubini Kananathan
 Submitted: Sep 6, 2018 3:14:52 PM
 Last Modified: Oct 8, 2018 12:10:00 PM
Revisions

Version: 11
 Submitted on: Oct 8, 2018 12:10:00 PM
 Submitted by: Sarubini Kananathan
 With comment: Automatically added model identifier BIOMD0000000708

Version: 9
 Submitted on: Oct 8, 2018 11:12:14 AM
 Submitted by: Sarubini Kananathan
 With comment: Automatically added model identifier BIOMD0000000708

Version: 7
 Submitted on: Oct 8, 2018 11:05:38 AM
 Submitted by: Sarubini Kananathan
 With comment: Automatically added model identifier BIOMD0000000708

Version: 6
 Submitted on: Sep 6, 2018 3:14:52 PM
 Submitted by: Sarubini Kananathan
 With comment: PubMed ID updated
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Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species  Initial Concentration/Amount 

I a 0000511 ; Aves 
1000.0 mol 
S h 0000514 ; Homo sapiens 
1000000.0 mol 
I h 0000511 ; Homo sapiens 
0.0 mol 
R h Recovered or Resolved ; Homo sapiens 
0.0 mol 
S a 0000514 ; Aves 
100000.0 mol 
Reactions
Reactions  Rate  Parameters 

S_a => I_a  Avian_population*beta_a*S_a*I_a  beta_a = 2.0E8 
S_h => I_h; I_a  beta_h*I_a*S_h  beta_h = 6.0E9 
I_a =>  Avian_population*mu_a*I_a  mu_a = 3.4246E4 
I_h =>  compartment*delta_h*I_h  delta_h = 0.3445 
=> S_h  compartment*pi_h  pi_h = 30.0 
I_h => R_h  compartment*gamma*I_h  gamma = 0.1 
S_h =>  compartment*mu_h*S_h  mu_h = 3.91E5 
Curator's comment:
(added: 08 Oct 2018, 11:05:23, updated: 08 Oct 2018, 13:16:58)
(added: 08 Oct 2018, 11:05:23, updated: 08 Oct 2018, 13:16:58)
Figure 3b of the reference publication has been reproduced. Simulation of the logistic growth 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.