Abstract
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.
Highlights
Great attention has been paid to the study of the traveling wave solutions in reaction-diffusion models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]
From Lemma 3 and Remark 4, we know that model (24) is a quasi-monotone nonincreasing system in (S, I) ∈ [Ê1, Ê2], and by using the monotone iteration scheme given in [3, 13], we can obtain the existence of the solution (S, I)T to the first two equations in model (24) for every c ≥ 2√R0 − 1, which satisfies (SI ((ξξ))) ≤ (SI ((ξξ))) ≤ (SI ((ξξ)))
We study the exponential decay rate of the traveling wave solution as ξ → −∞
Summary
Great attention has been paid to the study of the traveling wave solutions in reaction-diffusion models [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. We are interested in the existence of traveling wave solutions in the following reaction-diffusion epidemic model [20]: Since the traveling wave solution of model (14) has the following form
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