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