## Traveling wave solutions in a reaction-diffusion epidemic model.(English)Zbl 1291.35418

Summary: We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.

### MSC:

 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92D30 Epidemiology 35C07 Traveling wave solutions 35K57 Reaction-diffusion equations
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### References:

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