Title

Nonlocal Modeling Of Insect Borne Diseases

Keywords

Epidemiology; Existence and uniqueness; Fixed point; Integral equations; Nonlinear; Nonlocal; Pandemic; Yellow fever

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. © 2013 by Nova Science Publishers, Inc. All rights reserved.

Publication Date

3-1-2013

Publication Title

Fevers: Types, Treatments and Health Risks

Number of Pages

105-127

Document Type

Article; Book Chapter

Personal Identifier

scopus

Socpus ID

84891995951 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84891995951

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