Liu2017 - Dynamics of Avian Influenza with Logistic Growth

  public model
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: 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: Sarubini Kananathan
Modellers: Sarubini Kananathan

Metadata information

is (2 statements)
BioModels Database MODEL1808240002
BioModels Database BIOMD0000000708

isDescribedBy (1 statement)
PubMed 27887851

hasTaxon (2 statements)
Taxonomy Homo sapiens
Taxonomy Aves

hasProperty (2 statements)
Mathematical Modelling Ontology Ordinary differential equation model
Experimental Factor Ontology avian influenza

Curation status
Curated
Modelling approach(es)
ordinary differential equation model
Tags

Connected external resources

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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 public model Download this version
    • Submitted on: Oct 8, 2018 12:10:00 PM
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000708
  • Version: 9 public model Download this version
    • Submitted on: Oct 8, 2018 11:12:14 AM
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000708
  • Version: 7 public model Download this version
    • Submitted on: Oct 8, 2018 11:05:38 AM
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000708
  • Version: 6 public model Download this version
    • 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


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 = 2.0E-8
S_h => I_h; I_a beta_h*I_a*S_h beta_h = 6.0E-9
I_a => Avian_population*mu_a*I_a mu_a = 3.4246E-4
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 = 3.91E-5
Curator's comment:
(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.