An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases
We construct and analyze a nonlocal global pandemic model that comprises a system of two nonlocal integrodifferential equations (functional differential equations) and an ordinary differential equation. This model was constructed by considering a spherical coordinate transformation of a previously e...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2014/187685 |
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| _version_ | 1832548067049472000 |
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| author | John R. Cannon Daniel J. Galiffa |
| author_facet | John R. Cannon Daniel J. Galiffa |
| author_sort | John R. Cannon |
| collection | DOAJ |
| description | We construct and analyze a nonlocal global pandemic model that comprises a system of two nonlocal integrodifferential equations (functional differential equations) and
an ordinary differential equation. This model was constructed by considering a spherical coordinate transformation of a previously established epidemiology model that can be applied to insect-borne
diseases, like yellow fever. This transformation amounts to a nonlocal boundary value problem on the unit sphere and therefore can be interpreted as a global pandemic model for insect-borne diseases. We ultimately show that a weak solution to the weak formulation of this model exists using a fixed point argument, which calls upon the construction of a weak formulation and the existence
and uniqueness of an auxiliary problem. |
| format | Article |
| id | doaj-art-8d9b2cf144ab4b2fbe362bd61af064ad |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-8d9b2cf144ab4b2fbe362bd61af064ad2025-02-03T06:42:24ZengWileyInternational Journal of Differential Equations1687-96431687-96512014-01-01201410.1155/2014/187685187685An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne DiseasesJohn R. Cannon0Daniel J. Galiffa1Mathematics Department, University of Central Florida, Orlando, FL 32816, USADepartment of Mathematics, Penn State Erie, The Behrend College, Erie, PA 16563, USAWe construct and analyze a nonlocal global pandemic model that comprises a system of two nonlocal integrodifferential equations (functional differential equations) and an ordinary differential equation. This model was constructed by considering a spherical coordinate transformation of a previously established epidemiology model that can be applied to insect-borne diseases, like yellow fever. This transformation amounts to a nonlocal boundary value problem on the unit sphere and therefore can be interpreted as a global pandemic model for insect-borne diseases. We ultimately show that a weak solution to the weak formulation of this model exists using a fixed point argument, which calls upon the construction of a weak formulation and the existence and uniqueness of an auxiliary problem.http://dx.doi.org/10.1155/2014/187685 |
| spellingShingle | John R. Cannon Daniel J. Galiffa An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases International Journal of Differential Equations |
| title | An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases |
| title_full | An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases |
| title_fullStr | An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases |
| title_full_unstemmed | An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases |
| title_short | An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases |
| title_sort | existence theorem for a nonlocal global pandemic model for insect borne diseases |
| url | http://dx.doi.org/10.1155/2014/187685 |
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