| 19 | 0 | 47 |
| 下载次数 | 被引频次 | 阅读次数 |
研究了一类时空时滞的非局部扩散登革热传染病模型的行波解。通过构造上、下解和Schauder不动点定理研究了行波解的存在性，并借助分析技术得到了行波解在负无穷远处的渐近行为，将Laplace扩散登革热传染病模型行波解的研究结果推广到了时空时滞的非局部扩散模型。
Abstract：The traveling wave solutions to a class of dengue epidemic model with spatio-temporal delay and non-local dispersal is studied.The existence of traveling wave solutions is studied based on the the construction of upper and lower solutions and Schauder fixed point theorem,and the asymptotic behavior at negative infinity of traveling waves is obtained with analysis techniques,which extends the research results of traveling waves for dengue infectious disease models with Laplace diffusion to those non-local dispersal models with spatio-temporal delay.
[1]LIU Q,JIANG D Q,HAYAT T,et al.Stationary distribution and extinction of a stochastic dengue epidemic model[J].Journal of the Franklin Institute,2018,355(17):8891-8914.
[2]TRAORE A.Analysis of a vector-borne disease model with human and vectors immigration[J].Journal of applied mathematics and computing,2020,64(1/2):411-428.
[3]王凯，赵洪涌．一类具有时滞的反应扩散登革热传染病模型的行波解[J]．数学物理学报，2022,42(4):1209-1226.
[4]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.
[5]ZHANG R,LIU S Q.Traveling waves for SVIR epidemic model with nonlocal dispersal[J].Mathematical biosciences and engineering,2019,16(3):1654-1682.
[6]杨炜明，廖书，方芳．带有非局部扩散项的霍乱传染病模型行波解的存在性[J]．应用数学学报，2021,44(3):440-458.
[7]QIAO S X,YANG F Y,LI W T.Traveling waves of a nonlocal dispersal SEIR model with standard incidence[J].Nonlinear analysis:real world applications,2019,49:196-216.
[8]ZHU C C,LI W T,YANG F Y.Traveling waves in a nonlocal dispersal SIRH model with relapse[J].Computers&mathematics with applications,2017,73(8):1707-1723.
[9]LIAO S,YANG W M,FANG F.Traveling waves for a cholera vaccination model with nonlocal dispersal[J].Mathematical methods in the applied sciences,2021,44(6):5150-5171.
[10]BRITTON N F.Aggregation and the competitive exclusion principle[J].Journal of theoretical biology,1989,136(1):57-66.
[11]BRITTON N F.Spatial structures and periodic travelling waves in an integro-differential reactiondiffusion population model[J].SIAM journal on applied mathematics,1990,50(6):1663-1688.
[12]SMITH H L,THIEME H R.Strongly order preserving semiflows generated by functional differential equations[J].Journal of differential equations,1991,93(2):332-363.
[13]邹霞．具有时空时滞的非局部扩散SIR模型的行波解[J]．应用数学和力学，2018,39(5):611-630.
[14]YANG L,YANG Y R,SONG X.Traveling waves in a SIRH model with spatio-temporal delay and nonlocal dispersal[J].Acta mathematica scientia,2022,42(2):715-736.
[15]MA Z H,YUAN R.Traveling wave solutions of a nonlocal dispersal SIRS model with spatiotemporal delay[J].International journal of biomathematics,2017,10(5).DOI:10.1142/s1793524517500711.
[16]杨咏丽，杨赟瑞．非局部扩散的时空时滞霍乱传染病系统的行波解[J]．数学物理学报，2025,45(1):110-135.
[17]ZHOU J L,YANG Y.Traveling waves for a nonlocal dispersal SIR model with general nonlinear incidence rate and spatio-temporal delay[J].Discrete and continuous dynamical systems,series B,2017,22(4):1719-1741.
[18]YANG Y R,YANG Y,MA Z Y.Traveling waves for a nonlocal dispersal SIR model with renewal and spatio-temporal delay[J].Applicable analysis,2023,102(4/5):1038-1058.
[19]WU J H.Theory and applications of partial functional differential equations[M].New York:Springer,1996.
[20]WANG K,ZHAO H Y,WANG H,et al.Traveling wave of a reaction-diffusion vector-borne disease model with nonlocal effects and distributed delay[J].Journal of dynamics and differential equations,2023,35(4):3149-3185．
基本信息:
DOI：10.13486/j.issn.2097-4973.2026.02.013
中图分类号:O175;R181
引用信息:
[1]常梦飞,杨赟瑞.时空时滞的非局部扩散登革热传染病模型的单稳行波解[J].山东航空学院学报,2026,43(02):105-115.DOI:10.13486/j.issn.2097-4973.2026.02.013.
基金信息:
国家自然科学基金项目(12361038); 甘肃省基础研究创新群体项目(25JRRA805)
2026-04-15
2026-04-15