Liu2017 - Dynamics of Avian Influenza with Allee Growth Effect

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  • 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.
Submitter of the first revision: Sarubini Kananathan
Submitter of this revision: Sarubini Kananathan
Modellers: Sarubini Kananathan

Metadata information

is (2 statements)
BioModels Database MODEL1808240003
BioModels Database BIOMD0000000709

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


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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
  • Version: 7 public model Download this version
    • Submitted on: Oct 8, 2018 1:28:55 PM
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000709
  • Version: 5 public model Download this version
    • Submitted on: Aug 24, 2018 4:47:22 PM
    • Submitted by: Sarubini Kananathan
    • With comment: Model revised without commit message

(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions unpublished model revision of this model will only be shown to the submitter and their collaborators.

: Variable used inside SBML models

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 Rate Parameters
S_a => I_a Avian_population*beta_a*S_a*I_a beta_a = 1.8E-8
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 = 6.0E-9
S_h => compartment*mu_h*S_h mu_h = 3.91E-5
R_h => compartment*mu_h*R_h mu_h = 3.91E-5
=> S_a Avian_population*r_a*S_a*(1-S_a/M_a)*(S_a/m_a-1) 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)
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.