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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| Format: | Article |
| Language: | English |
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AIMS Press
2017-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017079 |
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| author | Xue Zhang Shuni Song Jianhong Wu |
| author_facet | Xue Zhang Shuni Song Jianhong Wu |
| author_sort | Xue Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-01db27f859654df0893cba693525fe44 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-01db27f859654df0893cba693525fe442025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61515153310.3934/mbe.2017079Onset and termination of oscillation of disease spread through contaminated environmentXue Zhang0Shuni Song1Jianhong Wu2College of Science, Northeastern University, Shenyang, Liaoning 110819, ChinaCollege of Science, Northeastern University, Shenyang, Liaoning 110819, ChinaCollege of Science, Northeastern University, Shenyang, Liaoning 110819, ChinaWe 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017079reaction-diffusion equationnonlocal delaydirichlet boundary conditionstabilityhopf bifurcation |
| spellingShingle | Xue Zhang Shuni Song Jianhong Wu Onset and termination of oscillation of disease spread through contaminated environment Mathematical Biosciences and Engineering reaction-diffusion equation nonlocal delay dirichlet boundary condition stability hopf bifurcation |
| title | Onset and termination of oscillation of disease spread through contaminated environment |
| title_full | Onset and termination of oscillation of disease spread through contaminated environment |
| title_fullStr | Onset and termination of oscillation of disease spread through contaminated environment |
| title_full_unstemmed | Onset and termination of oscillation of disease spread through contaminated environment |
| title_short | Onset and termination of oscillation of disease spread through contaminated environment |
| title_sort | onset and termination of oscillation of disease spread through contaminated environment |
| topic | reaction-diffusion equation nonlocal delay dirichlet boundary condition stability hopf bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017079 |
| work_keys_str_mv | AT xuezhang onsetandterminationofoscillationofdiseasespreadthroughcontaminatedenvironment AT shunisong onsetandterminationofoscillationofdiseasespreadthroughcontaminatedenvironment AT jianhongwu onsetandterminationofoscillationofdiseasespreadthroughcontaminatedenvironment |