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

John R. Cannon, Daniel Joseph Galiffa

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Article number187685
JournalInternational Journal of Differential Equations
Volume2014
DOIs
StatePublished - Jan 1 2014

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Existence Theorem
Weak Formulation
Spherical coordinates
Nonlocal Boundary Value Problems
Epidemiology
Nonlocal Equations
Model
Integrodifferential equations
Coordinate Transformation
Unit Sphere
Functional Differential Equations
Ordinary differential equations
Integro-differential Equation
Boundary value problems
Weak Solution
Ordinary differential equation
Existence and Uniqueness
Differential equations
Fixed point

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases. / Cannon, John R.; Galiffa, Daniel Joseph.

In: International Journal of Differential Equations, Vol. 2014, 187685, 01.01.2014.

Research output: Contribution to journalArticle

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