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

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  • John R. Cannon
  • Daniel J. Galiffa

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.

Suggested Citation

  • John R. Cannon & Daniel J. Galiffa, 2014. "An Existence Theorem for a Nonlocal Global Pandemic Model for Insect-Borne Diseases," International Journal of Differential Equations, Hindawi, vol. 2014, pages 1-10, July.
    • Handle: RePEc:hin:jnijde:187685
    DOI: 10.1155/2014/187685
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