一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解

Abstract

Abstract: This paper is concerned with the traveling waves of a nonlocal dispersal SIR epidemic model with delay and nonlinear incidence. The threshold dynamics are determined by the basic reproduction number R₀ and the minimal wave speed c^*. First, when c > c^*, R₀ > 1, the existence of the traveling waves is proved by applying Schauder's fixed point theorem and a limiting argument. Then, when 0 < c < c^*, R₀ > 1 or R₀ ≤ 1, the non-existence of traveling wave solutions is established by two-side Laplace transform.

Key words: Non-local dispersal, Traveling wave solution, SIR model, Schauder's fixed point theorem

CLC Number:

O175.14

Zou Xia, Wu Shiliang. Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence[J].Acta mathematica scientia,Series A, 2018, 38(3): 496-513.

Trendmd

References

[1] Kermack W O, Mckendrick A G. A contribution to the mathematical theory of epidemics. Proc Roy Soc London Ser B, 1927, 115(772):700-721
[2] Li J, Zou X. Modeling spatial spread of infectious disesses with a fixed latent period in a spatially continuous domain. Bull Math Bio, 2009, 71(8):2048-2079
[3] Hosono Y, llyas B. Traveling waves for a simple diffusive epidemic model. Math Models Methods Appl Sci, 1995, 5(7):935-966
[4] Wu C, Weng P. Asymptotic speed of propagation and traveling wavefronts for a SIR epidemic model. Discrete Contin Dyn Syst Ser B, 2011, 15:867-892
[5] Korobeinikov A. Global properties of infections disease models with nonlinear incidence. Bull Math Bio, 2007, 69(6):1871-1886
[6] Huang G, Takeuchi Y. Global analysis on delay epidemiological dynamic models with nonlinear incidence. J Math Bio, 2011, 63(1):125-139
[7] Bai Z, Wu S L. Traveling waves in a delayed SIR epidemic model with nonlinear incidence. Appl Math Comput, 2015, 263:221-232
[8] Murrary J D. Mathematical Biology, Ⅱ:Spatial Models and Biomedical Applications. New York:Springer, 2003
[9] Carr J, Chmaj A. Uniqueness of traveling waves for nonlocal monostable equations. Proc Am Math Soc, 2004, 132:2433-2439
[10] Coville J, Davila J, Martinez S. Pulsating fronts for nonlocal dispersion and KPP nonlinearity. Ann Inst H Poincare Anal Non Lineaire, 2013, 30(2):179-223
[11] Li W T, Yang F Y. Traveling waves for a nonlocal dispersal SIR model with standard incidence. J Integral Equ Appl, 2014, 26(2):243-273
[12] Yang F Y, Li Y, Li W T, Wang Z C. Traveling waves in a nonlocal dispersal Kermack-Mckendrick epidemic model. Discrete Cont Dyn Syst B, 2013, 18(7):1969-1993
[13] Li Y, Li W T, Yang F Y. Traveling waves for a nonlocal dispersal SIR model with delay and external supplies. Appl Math Comput, 2014, 247:723-740
[14] Wang Z C, Wu J. Traveling waves of a diffusive Kermack-Mckendrick epidemic model with non-local delayed transmission. Proc R Soc Lond Ser A, 2010, 466:237-261
[15] Wang Z C, Wu J, Liu R. Traveling waves of the spread of avian influenza. Proc Amer Math Soc, 2012, 140(11):3931-3946
[16] Wang Z C, Wu J. Traveling waves in a bio-reactor model with stage-structure. J Math Anal Appl, 2012, 385(2):683-692
[17] Widder D V. The Laplace Transform. Princeton:Princeton University Press, 1942
[18] Thieme H R, Zhao X Q, Asymptotic speeds of spread and traveling waves for integral equations and delayed reaction-diffusion models. J Differential Equations, 2003, 195(2):430-470

Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Delay and Nonlinear Incidence

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 3

Metrics

Comments

Recommended 10

[1]	Lou Cuijuan, Yang Yin. Existence of Traveling Wave Solutions for a Classical Chemotaxis Model [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1044-1058.
[2]	ZHANG Wei-Guo, LIU Qiang, LI Zheng-Ming, LI Xiang. BOUNDED TRAVELING WAVE SOLUTIONS OF VARIANT BOUSSINESQ EQUATION WITH A DISSIPATION TERM AND DISSIPATION EFFECT [J]. Acta mathematica scientia,Series A, 2014, 34(3): 941-959.
[3]	LIU Chun-Ping. Explicit Traveling Wave Solutions for Some Nonlinear Evolution Equations [J]. Acta mathematica scientia,Series A, 2004, 4(6): 661-668.