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Multi-type Entire Solutions in a Nonlocal Dispersal Epidemic Model

机译：非局部扩散流行病模型中的多类型整体解

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This paper deals with entire solutions of a nonlocal dispersal epidemic model. Unlike local (random) dispersal problems, a nonlocal dispersal operator is not compact and the solutions of nonlocal dispersal system studied here lack regularity in suitable spaces, which affects the uniform convergence of the solution sequences and the technique details in constructing the entire solutions. In the monostable case, some new types of entire solutions are constructed by combining leftward and rightward traveling fronts with different speeds and a spatially independent solution. In the bistable case, the existence of many different entire solutions with merging fronts are proved by constructing different sub- and super-solutions. Various qualitative features of the entire solutions are also investigated. A key idea is to characterize the asymptotic behaviors of the traveling wave solutions at infinite in terms of appropriate sub- and super-solutions. Finally, we also obtain the smoothness of the entire solutions in space, i.e., the solutions established in our paper are global Lipschitz continuous in space.
机译：本文讨论了非局部扩散流行模型的整体解决方案。与局部（随机）分散问题不同，非局部分散算子不是紧凑的，此处研究的非局部分散系统的解在适当的空间中缺乏规则性，这影响了解序列的均匀收敛以及构造整个解的技术细节。在单稳态情况下，通过将具有不同速度的左，右行进线与空间独立的解决方案相结合，构造了一些新型的整体解决方案。在双稳态情况下，通过构造不同的子解和超解证明了存在许多具有合并前沿的整个解。还研究了整个解决方案的各种定性特征。一个关键的想法是根据适当的子解和超解来刻画无穷大行波解的渐近性质。最后，我们还获得了整个空间解的平滑度，即，本文中建立的解是全局Lipschitz空间连续的。

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