Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence

ZHANG Qiu; CHEN Guangsheng

doi:10.21656/1000-0887.390208

Volume 40 Issue 7

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ZHANG Qiu, CHEN Guangsheng. Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence[J]. Applied Mathematics and Mechanics, 2019, 40(7): 713-727. doi: 10.21656/1000-0887.390208

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Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence

doi: 10.21656/1000-0887.390208

School of Mathematics and Statistics, Xidian University, Xi’an 710071, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(11671315)

Received Date: 2018-07-26
Rev Recd Date: 2018-11-09
Publish Date: 2019-07-01

Abstract

Abstract

The existence of traveling wave solutions for nonlocal dispersal SIR epidemic models with delay was studied. Firstly, the boundedness of I was proved by contradiction. Then according to the boundedness of I, the existence of traveling waves with c>c^* was established. Secondly, through further analysis of traveling waves with super-critical speeds, the existence of traveling waves with the critical speed was derived. Finally, the influence of basic reproduction number R⁰ on the existence of c>c^* was discussed.
- traveling wave solution,
- critical wave speed,
- nonlocal dispersal,
- basic reproduction number

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References(20)

References

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