TRAVELING WAVES IN A SIRH MODEL WITH SPATIO-TEMPORAL DELAY AND NONLOCAL DISPERSAL

doi:10.1007/s10473-022-0218-5

Abstract

Abstract: This paper deals mainly with the existence and asymptotic behavior of traveling waves in a SIRH model with spatio-temporal delay and nonlocal dispersal based on Schauder's fixed-point theorem and analysis techniques, which generalize the results of nonlocal SIRH models without relapse and delay. In particular, the difficulty of obtaining the asymptotic behavior of traveling waves for the appearance of spatio-temporal delay is overcome by the use of integral techniques and analysis techniques. Finally, the more general nonexistence result of traveling waves is also included.

Key words: Nonlocal dispersal, spatio-temporal delay, traveling waves

CLC Number:

35K57

Lu YANG, Yun-Rui YANG, Xue SONG. TRAVELING WAVES IN A SIRH MODEL WITH SPATIO-TEMPORAL DELAY AND NONLOCAL DISPERSAL[J].Acta mathematica scientia,Series B, 2022, 42(2): 715-736.

Trendmd

References

[1] Aronson D G, Weinberger H F. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation. Partial Differential Equations and Related Topics, 1975, 446:5-49
[2] Fife P C, Mcleod J B. The approach of solutions of nonlinear diffusion equations to traveling front solutions. Arch Rational Mech Anal, 1977, 65:335-361
[3] Ducrot A, Magal P, Ruan S G. Travelling wave solutions in multigroup age-structured epidemic models. Arch Rational Mech Anal, 2010, 195(1):311-331
[4] Wang X S, Wang H Y, Wu J H. Traveling waves of diffusive predator-prey systems:disease outbreak propagation. Discrete and Continuous Dynamical Systems, 2012, 32(9):3303-3324
[5] Zhang T R, Wang W D, Wang K F. Minimal wave speed for a class of non-cooperative diffusion-reaction system. J Differential Equations, 2016, 260(3):2763-2791
[6] Medlock J, Kot M. Spreading disease:integro-differential equtions old and new. Mathematical Biosciences, 2003, 184(2):201-222
[7] Coville J, Dupaigne L. Propagation speed of travelling fronts in nonlocal reaction-diffusion equations. Nonl Anal, 2005, 60(5):797-819
[8] Yang F Y, Li Y, Li W T, Wang Z C. Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model. Discrete and Continuous Dynamical Systems Series B, 2013, 18(7):1969-1993
[9] Li W T, Yang F Y. Traveling waves for a nonlocal dispersal SIR model with standard incidence. Journal of Integral Equations and Applications, 2014, 26(2):243-273
[10] Yang F Y, Li W T. Traveling waves in a nonlocal dispersal SIR model with critical wave speed. J Math Anal Appl, 2018, 458(2):1131-1146
[11] Yang F Y, Li W T, Wang J B. Wave propagation for a class of non-local dispersal non-cooperative systems. Proceedings of the Royal Society of Edinburgh Section A Mathematics, 2019, 150(4):1-33
[12] Zhu C C, Li W T, Yang F Y. Traveling waves in a nonlocal dispersal SIRH model with relapse. Computers and Mathematics with Applications, 2017, 73(8):1707-1723
[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(15):723-740
[14] Zhang S P, Yang Y R, Zhou Y H. Traveling waves in a delayed SIR model with nonlocal dispersal and nonlinear incidence. J Math Phys, 2018, 59(1):011513
[15] Yang Y, Yang Y R, Jiao X J. Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence. Electronic research archive, 2020, 28(1):1-13
[16] Britton N F. Aggregation and the competitive exclusion principle. J Theoret Biol, 1989, 136(1):57-66
[17] Britton N F. Spatial structures and periodic travelling waves in an integro-differential reaction-diffusion population model. SIAM J Appl Math, 1990, 50(6):1663-1688
[18] Smith H L, Thieme H R. Strongly order preserving semiflows generated by functional differential equations. J Differential Equations, 1991, 93(2):332-363
[19] Wang J B, Li W T, Yang F Y. Traveling waves in a nonlocal dispersal SIR model with nonlocal delayed transmission. Communications in Nonlinear Science and Numerical Simulation, 2015, 27(1/3):136-152
[20] Wu S L, Ruan S G. Entire solutions for nonlocal dispersal equations with spatio-temporal delay:Monostable case. J Differential Equations, 2015, 258(7):2435-2470
[21] Ma Z H, Yuan R. Traveling wave solutions of a nonlocal dispersal SIRS model with spatio-temporal delay. International Journal of Biomathematics, 2017, 10(5):1-23
[22] Zhou X. Traveling wave solutions for nonlocal dispersal SIR models with spatio-temporal delays. Applied Mathematics and Mechanics, 2018, 39(5):611-630
[23] Su S, Zhang G B. Traveling waves of a nonlocal dispersal equation with spatio-temporal delay. Journal of Lanzhou University of Arts and Science (Natural Sciences), 2020, 34(3):9-13
[24] Yang Y R, Yang Y, Ma Z Y. Traveling waves for a nonlocal dispersal SIR model with renewal and spatio-temporal delay. Applicable Analysis, 2021. https://www.tandfonline.com/doi/full/10.1080/00036811.2021.1969369