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An epidemiology model suggested by yellow fever
Author(s) -
Can John R.,
Galiffa Daniel J.
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1556
Subject(s) - uniqueness , mathematics , construct (python library) , ordinary differential equation , argument (complex analysis) , a priori and a posteriori , nonlinear system , epidemic model , differential equation , work (physics) , calculus (dental) , mathematical analysis , computer science , medicine , mechanical engineering , philosophy , physics , dentistry , epistemology , quantum mechanics , engineering , programming language , population , environmental health
In this work, 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, 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 © 2011 John Wiley & Sons, Ltd.