An epidemiology model suggested by yellow fever

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.