| 摘要: |
| 针对霍乱传染病具有人与人之间的直接传播和人与被污染水源之间的非直接传播这一多种传播途径的特点，创新性地构造出一个带扩散项的偏微分方程组模型，并求解出该模型的平衡点和基本再生数；行波解是传染病模型中的一个关键因素，为解决该模型行波解的存在性问题，提出上下解的构造方法；在模型中方程个数和参数较多，上下解不易构造的情况下，通过对该模型在无病平衡点处的线性化，利用上下解的构造方法构造出明确的上解和下解，并讨论上解和下解函数中参数的取值范围，重点分别验证此上解和下解满足模型上下解和边界条件，以此利用不动点定理得出行波解的存在性。 |
| 关键词: 霍乱 行波解 上下解方法 |
| DOI： |
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| Calculation of Upper and Lower Solutions of Travelling Wave Solutions for Cholera Diseases |
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QIN Shuang-yu
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School of Mathematics and Statistics，Chongqing Technology and Business University，Chongqing 400067，China
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| Abstract: |
| In view of the characteristics of cholera direct spreading between people and indirect diffusing between people and polluted water sources， a partial differential equation system model with diffusion term was constructed creatively， and the equilibrium point and basic regeneration number of the model were solved. Traveling wave solution is one of the key factors in epidemic model. In order to solve the existence of traveling wave solution， the construction method of upper and lower solutions is proposed. In the case that there are so many equations and parameters in the model and that the upper and lower solutions are not easy to construct， by linearizing the model at the disease-free equilibrium point， the explicit upper and lower solutions are constructed by using the construction method of upper and lower solutions， and the range of parameters in the upper solutions and lower solutions function is discussed.The emphasis is to verify that the upper and lower solutions satisfy the upper and lower solutions and boundary conditions of the model respectively.So the existence of traveling wave solutions is obtained by using the fixed point theorem. |
| Key words: cholera traveling wave solution upper and lower solutions method |
