Open AccessOnset and termination of oscillation of disease spread through contaminated environment
Author(s) -
Xue Zhang,
Sanghoon Song,
Jianhong Wu
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017079
Subject(s) - nonlinear system , boundary value problem , dirichlet boundary condition , oscillation (cell signaling) , control theory (sociology) , mathematics , statistical physics , physics , computer science , mathematical analysis , biology , control (management) , quantum mechanics , artificial intelligence , genetics
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.