An epidemiology model suggested by yellow fever

    Authors

    J. R. Cannon;D. J. Galiffa

    Comments

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    Abbreviated Journal Title

    Math. Meth. Appl. Sci.

    Keywords

    epidemiology; existence and uniqueness; fixed point; nonlinear; nonlocal; yellow fever; integral equations; REACTION-DIFFUSION SYSTEM; ASYMPTOTIC SPEED; INTEGRAL-EQUATIONS; TRAVELING-WAVES; SPREAD; STABILIZATION; POPULATIONS; Mathematics, Applied

    Abstract

    In this work, we construct and analyze a nonlinear reactiondiffusion epidemiology model consisting of two integral-differential equations and an ordinary differential equation, which is suggested by various insect borne diseases, for example, Yellow Fever. We begin by defining a nonlinear auxiliary problem and establishing the existence and uniqueness of its solution via a priori estimates and a fixed point argument, from which we prove the existence and uniqueness of the classical solution to the analytic problem. Next, we develop a finite-difference method to approximate our model and perform some numerical experiments. We conclude with a brief discussion of some subsequent extensions. Copyright (C) 2011 John Wiley & Sons, Ltd.

    Journal Title

    Mathematical Methods in the Applied Sciences

    Volume

    35

    Issue/Number

    2

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    196

    Last Page

    206

    WOS Identifier

    WOS:000299546500008

    ISSN

    0170-4214

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