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Traveling waves and entire solutions for an epidemic model with asymmetric dispersal

  • Author Bio: xuwb08@lzu.edu.cn(W.-B. Xu); zhangl13@lzu.edu.cn(L. Zhang)
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  • This paper is concerned with traveling waves and entire solutions of one epidemic model with asymmetric dispersal kernel function arising from the spread of an epidemic by oral-faecal transmission. The asymmetry of the kernel function will have an influence on two aspects: (ⅰ) the minimal wave speed of traveling wave fronts may be nonpositive, but we give a new restrictive condition on the kernel function to guarantee it is positive; (ⅱ) the two traveling wave solutions with the same speed spreading from right and left of $x$-axis may be different in shape, which further makes that the entire solutions with five or four parameters may be asymmetric and the entire solutions with three parameters increasing in $x$ may be different from those decreasing in $x$ in shape. As for traveling wave solutions, we get the existence, asymptotic behavior and uniqueness of the two traveling wave solutions spreading from right and left of $x$-axis, respectively. We further construct three new entire solutions with five, four or three parameters. Two comparison principles also be established.

    Mathematics Subject Classification: 35K57, 35R20, 92D25.


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