Liu2017 - Dynamics of Avian Influenza with Allee Growth Effect

  public model
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
  • 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
Sarubini Kananathan

Metadata information

hasTaxon
Taxonomy Homo sapiens
8782
isDescribedBy
hasProperty
Mathematical Modelling Ontology Ordinary differential equation model
0005222
Curation status
Curated
Name Description Size Actions

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: 24-Aug-2018 16:47:22
  • Last Modified: 08-Oct-2018 13:28:55
Revisions
  • Version: 7 public model Download this version
    • Submitted on: 08-Oct-2018 13:28:55
    • Submitted by: Sarubini Kananathan
    • With comment: Automatically added model identifier BIOMD0000000709
  • Version: 5 public model Download this version
    • Submitted on: 24-Aug-2018 16:47:22
    • Submitted by: Sarubini Kananathan
    • With comment: Model revised without commit message
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.