An epidemiology model suggested by yellow fever
Abbreviated Journal Title
Math. Meth. Appl. Sci.
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
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.
Mathematical Methods in the Applied Sciences
"An epidemiology model suggested by yellow fever" (2012). Faculty Bibliography 2010s. 2350.