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International Journal of Differential Equations
Volume 2014 (2014), Article ID 187685, 10 pages
http://dx.doi.org/10.1155/2014/187685
Research Article

An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases

1Mathematics Department, University of Central Florida, Orlando, FL 32816, USA
2Department of Mathematics, Penn State Erie, The Behrend College, Erie, PA 16563, USA

Received 6 May 2014; Revised 14 July 2014; Accepted 15 July 2014; Published 24 July 2014

Academic Editor: Kanishka Perera

Copyright © 2014 John R. Cannon and Daniel J. Galiffa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.