Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence

Yang Yang; Yun-Rui Yang; Xin-Jun Jiao; Yang Yang; Yun-Rui Yang; Xin-Jun Jiao

doi:10.3934/era.2020001

Electronic Research Archive

2020, Volume 28, Issue 1: 1-13. doi: 10.3934/era.2020001

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Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou, Gansu 730070, China

Received: 01 September 2019 Revised: 01 December 2019
35K57, 35R20, 92D25

In this paper, the existence and non-existence of traveling wave solutions are established for a nonlocal dispersal SIR model equipped delay and generalized incidence. In addition, the existence and asymptotic behaviors of traveling waves under critical wave speed are also contained. Especially, the boundedness of traveling waves is obtained completely without imposing additional conditions on the nonlinear incidence.
- Nonlocal dispersal,
- traveling waves,
- delay
Citation: Yang Yang, Yun-Rui Yang, Xin-Jun Jiao. Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence[J]. Electronic Research Archive, 2020, 28(1): 1-13. doi: 10.3934/era.2020001

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Abstract

In this paper, the existence and non-existence of traveling wave solutions are established for a nonlocal dispersal SIR model equipped delay and generalized incidence. In addition, the existence and asymptotic behaviors of traveling waves under critical wave speed are also contained. Especially, the boundedness of traveling waves is obtained completely without imposing additional conditions on the nonlinear incidence.

References

[1]	Nonlinear diffusion in population genetics, combusion, and nerve pulse propagation. Partial Differential Equations and Related Topics (1975) 446: 5-49.
[2]	Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. (1978) 30: 33-76.
[3]	Traveling waves in a delayed SIR epidemic model with nonlinear incidence. Applied Mathematics and Computation (2015) 263: 221-232.
[4]	Propagation speed of traveling fronts in nonlocal reaction-diffusion equation. Nonl. Anal. (2005) 60: 797-819.
[5]	Travelling wave solutions in multigroup age-structure epidemic models. Arch. Ratinal Mech. Anal. (2010) 195: 311-331.
[6]	Travelling wave solutions for an infection-age structured model with diffusion. Proc. Roy. Soc. Edinburgh Sect. A Math. (2009) 139: 459-482.
[7]	The approach of solutions nonlinear diffusion equations to traveling front solutions. Arch. Ratinal Mech. Anal. (1977) 65: 335-361.
[8]	Spatial dynamics of the diffusive logistic equation with a sedentary compartment. Can. Appl. Math. Q. (2002) 10: 473-499.
[9]	A contribution to the mathematical theory of epidemics. Proc. Roy. Soc. Lond. Ser. B (1927) 115: 700-721.
[10]	Spatial dynamics of a nonlocal dispersal population model in a shifting environment. Journal of Nonlinear Science (2018) 28: 1189-1219.
[11]	Traveling waves for a nonlocal dispersal SIR model with standard incidence. Journal of Integral Equations and Applications (2014) 26: 243-273.
[12]	Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission. Communications in Nonlinear Science and Numerical Simulation (2015) 27: 136-152.
[13]	Travelling waves of diffusive predator-pery systems: Disease outbreak propagation. Discrete Cont. Dyn. Syst. (2012) 32: 3303-3324.
[14]	Travelling waves of a diffiusive Kermack-McKendrick epidemic model with non-local delayed transmission. Proc. Roy. Soc. Lond. Ser. A Math. Phys. Eng. Sci. (2010) 466: 237-261.
[15]	(1941) The Laplace Transform. Princeton, NJ: Princeton University Press.
[16]	Entire solutions for nonlocal dispersal equations with spatio-temporal delay: Monostable case. J. Differential Equations (2015) 258: 2435-2470.
[17]	Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model. Discrete Cont. Dyn. Syst. Ser. B (2013) 18: 1969-1993.
[18]	Traveling waves in a nonlocal dispersal SIR model with critical wave speed. J. Math. Anal. Appl. (2018) 458: 1131-1146.
[19]	S. P. Zhang, Y. R. Yang and Y. H. Zhang, Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence, J. Math. Phys., 59 (2018), 011513, 15pp. doi: 10.1063/1.5021761
[20]	Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity. J. Differential Equations (2012) 252: 5096-5124.
[21]	Traveling waves in a nonlocal dispersal SIR epidemic model with delay and nonlinear incidence. Acta Mathematica Scientia (2018) 38: 496-513.

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