Zhang Tianran, Gou Qingming
School of Mathematics and Statistics, Southwest University, Chongqing 400715, China.
College of Mathematics & Computer Science, Yangtze Normal University, Chongqing 408100, China.
ScientificWorldJournal. 2014;2014:409730. doi: 10.1155/2014/409730. Epub 2014 Apr 27.
Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c (∗) is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations.
基于科德索(Codeço)2001年的霍乱模型,提出了一个包含病原体扩散和疾病相关死亡的霍乱流行模型。给出了最小波速c(∗)的公式。为了证明行波解的存在性,通过上下解构造了一个不变锥,并应用了绍德尔不动点定理。通过双边拉普拉斯变换证明了行波解的不存在性。然而,要应用双边拉普拉斯变换,需要行波解指数衰减的先验估计。为此,提出了一种新方法,该方法可应用于由三个以上方程组成的反应扩散系统。