Nonlocal modeling of insect borne diseases

Daniel Joseph Galiffa, John R. Cannon

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations

Abstract

We construct and analyze a nonlinear reaction-diffusion epidemiology model consisting of two integral-differential equations and an ordinary differential equation, which is suggested by various insect borne diseases like Yellow Fever. We first define a nonlinear auxiliary problem and establish the existence and uniqueness of its solution via a priori estimates and a fixed point argument. This leads to the existence and uniqueness of the classical solution to the analytic problem. We then develop a finite-difference method to approximate our model and conduct some numerical experiments, which demonstrate the biological applicability of the model. A large portion of this analysis originally appeared in: Cannon, J.R. and Galiffa, D.J. An Epidemiology Model Suggested by Yellow Fever. Math. Methods Appl. Sci. 2012, 35, 196-206. We supplement the analysis of the aforesaid paper by discussing ways to enhance the model therein and describe an open problem. We then conclude this chapter with an extension that yields a nonlocal global pandemic model for insect borne diseases, which is the first of its kind, and also give some preliminary results and future considerations.

Original languageEnglish (US)
Title of host publicationFevers: Types, Treatments and Health Risks
PublisherNova Science Publishers, Inc.
Pages105-127
Number of pages23
ISBN (Print)9781624177989
StatePublished - Mar 2013

All Science Journal Classification (ASJC) codes

  • Medicine(all)

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