Haiqin Zhao
Abstract:
In this article we study the traveling wave solutions of a monostable
nonlocal reaction-diffusion system with delay arising from
the spread of an epidemic by oral-faecal transmission.
From [23], there exists a minimal wave speed
such that a
traveling wave solution exists if and only if the wave speed is above
.
In this article, we first establish the exact asymptotic behavior of the
traveling waves at
.
Then, we construct some annihilating-front
entire solutions which behave like a traveling wave front propagating from
the left side (or the right side) on the x-axis or two traveling wave fronts
propagating from both sides on the x-axis as
and converge
to the unique positive equilibrium as
.
From the viewpoint of epidemiology, these results provide some new spread
ways of the epidemic.
Submitted December 20, 2016. Published June 30, 2017.
Math Subject Classifications: 35K57, 35B05, 35B40, 92D30.
Key Words: Traveling wave front; epidemic model; reaction-diffusion system;
monostable nonlinearity.
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Haiqin Zhao School of Mathematics and Statistics Xidian University Xi'an, Shaanxi 710071, China email: zhaohaiqin@xidian.edu.cn Phone: 0086-02981891379 |
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