Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence
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摘要: 研究了一类具有时滞的非局部扩散SIR传染病模型的行波解。首先, 利用反证法证明了I是有界的, 并根据I的有界性研究了波速c>c*时行波解(波速大于最小波速的行波)的存在性。其次,利用c>c*的行波的存在性结果证明了临界波(波速等于最小波速的行波)的存在性。最后, 讨论了R0对临界波存在性的影响.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.
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[1] VAN DEN DRIESSCHE P, WATMOUGH J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission[J]. Mathematical Biosciences,2002,180(1/2): 29-48. [2] YANG F Y, LI Y, LI W T, et al. Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model[J]. Discrete and Continuous Dynamical Systems(Series B),2013,18(7): 1969-1993. [3] WANG H Y. Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems[J]. Journal of Nonlinear Science,2011,21(5): 747-783. [4] WANG H Y, WANG X S. Traveling wave phenomena in a Kermack-Mckendrick SIR model[J]. Journal of Dynamics & Differential Equations,2016,28(1):143-166. [5] WANG J B, LI W T, YANG F Y. Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission[J]. Communications in Nonlinear Science & Numerical Simulations,2015,27(1/3):136-152. [6] FU S C, GUO J S, WU C C. Traveling wave solutions for a discrete diffusive epidemic model[J]. Journal of Nonlinear and Convex Analysis,2016,17(9): 1739-1751. [7] ZHANG T R, WANG W D, WANG K F. Minimal wave speed for a class of non-cooperative diffusion-reaction system[J]. Journal of Differential Equations,2016,260(3): 2763-2791. [8] WANG X S, WANG H Y, WU J H. Traveling waves of diffusive predator-prey systems: disease outbreak propagation[J]. Discrete & Continuous Dynamical Systems,2017,32(9): 3303-3324. [9] LI Y, LI W T, YANG F Y. Traveling waves for a nonlocal dispersal SIR model with delay and external supplies[J]. Applied Mathematics & Computation,2014,247: 723-740. [10] LI Y, LI W T, LIN G. Traveling waves of a delayed diffusive SIR epidemic model[J]. Communications on Pure & Applied Analysis,2015,14(3): 1001-1022. [11] WANG Z C, WU J H. Travelling waves of a diffusive Kermack-McKendrick epidemic model with non-local delayed transmission[J]. Proceedings Mathematical Physical & Engineering Sciences,2010,466(2113): 237-261. [12] LI W T, YANG F Y, MA C, et al. Traveling wave solutions of a nonlocal delayed SIR model without outbreak threshold[J]. Discrete and Continuous Dynamical Systems(Series B),2014,19(2): 467-484. [13] BAI Z G, WU S L. Traveling waves in a delayed SIR epidemic model with nonlinear incidence[J]. Applied Mathematics and Computation,2015,263: 221-232. [14] 邹霞, 吴事良. 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[J]. 数学物理学报, 2018,38(3): 496-513.(ZOU Xia, WU Shiliang. Traveling waves in a nonlocal dispersal SIR epidemic model with delay and nonlinear incidence[J]. Acta Mathematica Scientia,2018,38(3): 496-513.(in Chinese)) [15] ZHANG S P, YANG Y R, ZHOU Y H. Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence[J]. Journal of Mathematical Physics,2018,59(1): 011513. DOI: 10.1063/1.5021761. [16] CHEN Y Y, GUO J S, HAMEL F. Traveling waves for a lattice dynamical system arising in a diffusive endemic model[J]. Nonlinearity,2016,30(6). DOI: 10.1088/1361-6544/aa6b0a. [17] YANG F Y, LI W T. Traveling waves in a nonlocal dispersal SIR model with critical wave speed[J]. Journal of Mathematical Analysis & Applications,2017,458(2): 1131-1146. [18] WU C C. Existence of traveling waves with the critical speed for a discrete diffusive epidemic model[J]. Journal of Differential Equations,2017,262(1): 272-282. [19] ZHANG G B, LI W T, WANG Z C. Spreading speeds and traveling waves for nonlocal dispersal equations with degenerate monostable nonlinearity[J]. Journal of Differential Equations,2012,252(9): 5096-5124. [20] CAPASSO V, SERIO G. A generalization of the Kermack-McKendrick deterministic epidemic model[J]. Mathematical Biosciences,1978,42(1/2): 43-61.
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