TRAVELING WAVES OF A NONLOCAL DIFFUSION SIRS EPIDEMIC MODEL WITH A CLASS OF NONLINEAR INCIDENCE RATES AND TIME DELAY

Weifang Yan

doi:10.11948/2156-907X.20170135

2019 Volume 9 Issue 2

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Weifang Yan. TRAVELING WAVES OF A NONLOCAL DIFFUSION SIRS EPIDEMIC MODEL WITH A CLASS OF NONLINEAR INCIDENCE RATES AND TIME DELAY[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 452-474. doi: 10.11948/2156-907X.20170135

Citation:

Weifang Yan. TRAVELING WAVES OF A NONLOCAL DIFFUSION SIRS EPIDEMIC MODEL WITH A CLASS OF NONLINEAR INCIDENCE RATES AND TIME DELAY[J]. Journal of Applied Analysis & Computation, 2019, 9(2): 452-474. doi: 10.11948/2156-907X.20170135

TRAVELING WAVES OF A NONLOCAL DIFFUSION SIRS EPIDEMIC MODEL WITH A CLASS OF NONLINEAR INCIDENCE RATES AND TIME DELAY

Weifang Yan

School of Mathematics and Statistics Science, Ludong University, Yantai 264025, China

Author Bio: Email address:yanwf1988@126.com(W. Yan)
Fund Project: The author was supported by Natural Science Foundation of Shandong Province (No. ZR2015PA004) and Scientific Research Foundation of Ludong University (No. LY2015003)

Abstract

Abstract

In this paper, we study the traveling waves of a delayed SIRS epidemic model with nonlocal diffusion and a class of nonlinear incidence rates. When the basic reproduction ratio $ \mathscr{R}_0>1 $, by using the Schauder's fixed point theorem associated with upper-lower solutions, we reduce the existence of traveling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of traveling wave solutions connecting the disease-free steady state and the endemic steady state. When $ \mathscr{R}_0<1 $, the nonexistence of traveling waves is obtained by the comparison principle.
- SIRS /
- traveling waves /
- nonlocal diffusion /
- nonlinear incidence rates /
- upper-lower solutions
MSC: 34B40, 35C07, 92D30

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References

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