An epidemiology model suggested by yellow fever. (English) Zbl 1232.92056

Cannon, John R.; Galiffa, Daniel J.

Math. Methods Appl. Sci. 35, No. 2, 196-206 (2012).

Summary: 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.

MSC:

92C60	Medical epidemiology
45K05	Integro-partial differential equations
35K57	Reaction-diffusion equations
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65R20	Numerical methods for integral equations
65D30	Numerical integration
92D30	Epidemiology
37N25	Dynamical systems in biology

Keywords:

existence; uniqueness; fixed point; nonlinear; nonlocal; integral equations

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