An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases. (24th July 2014)

• Record Type: Journal Article
• Authors: Cannon, John R.; Galiffa, Daniel J.
• Other Names: Perera Kanishka Academic Editor.
• Is Part Of: International journal of differential equations. Volume 2014(2014)
• Publication Date: 2014-07-24
• Subjects: Differential equations -- Periodicals; Differential equations; Periodicals; 515.35
• DOI: 10.1155/2014/187685
• Languages: English
• ISSNs: 1687-9643

Abstract

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.