Onset and termination of oscillation of disease spread through contaminated environment

We consider a reaction diffusion equation with a delayed nonlocal nonlinearity and subject to Dirichlet boundary condition. The model equation is motivated by infection dynamics of disease spread (avian influenza, for example) through environment contamination, and the nonlinearity takes into accoun...

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Published inMathematical biosciences and engineering : MBE Vol. 14; no. 5-6; pp. 1515 - 1533
Main Authors Zhang, Xue, Song, Shuni, Wu, Jianhong
Format Journal Article
LanguageEnglish
Published United States AIMS Press 01.10.2017
Subjects
Algorithms
Animals
Birds
Communicable Disease Control
Computer Simulation
dirichlet boundary condition
Disease Outbreaks
Environment
Epidemics
hopf bifurcation
Humans
Influenza in Birds - epidemiology
Influenza in Birds - transmission
Models, Biological
Models, Statistical
Nonlinear Dynamics
nonlocal delay
Oscillometry
reaction-diffusion equation
stability
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Summary:We consider a reaction diffusion equation with a delayed nonlocal nonlinearity and subject to Dirichlet boundary condition. The model equation is motivated by infection dynamics of disease spread (avian influenza, for example) through environment contamination, and the nonlinearity takes into account of distribution of limited resources for rapid and slow interventions to clean contaminated environment. We determine conditions under which an equilibrium with positive value in the interior of the domain (disease equilibrium) emerges and determine conditions under which Hope bifurcation occurs. For a fixed pair of rapid and slow response delay, we show that nonlinear oscillations can be avoided by distributing resources for both fast or slow interventions.
ISSN:1551-0018
DOI:10.3934/mbe.2017079