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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:
92C60Medical epidemiology
45K05Integro-partial differential equations
35K57Reaction-diffusion equations
65M06Finite difference methods (IVP of PDE)
65R20Integral equations (numerical methods)
65D30Numerical integration
92D30Epidemiology
37N25Dynamical systems in biology