American Institute of Mathematical Sciences

Advanced
November  2005, 5(4): 1043-1056. doi: 10.3934/dcdsb.2005.5.1043

Asymptotic speed of spread and traveling waves for a nonlocal epidemic model

Dashun Xu 1, and  Xiao-Qiang Zhao 2,

1. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NF A1C 5S7, Canada
2. 

Department of Mathematics and Statistics, Memorial University of Newfoundland, St. Johns, NF A1C 5S7

Received  December 2004 Revised  July 2005 Published  August 2005

By applying the theory of asymptotic speeds of spread and traveling waves to a nonlocal epidemic model, we established the existence of minimal wave speed for monotone traveling waves, and show that it coincides with the spreading speed for solutions with initial functions having compact supports. The numerical simulations are also presented.
Keywords: traveling waves, Spreading speed, nonlocal epidemic model..
Mathematics Subject Classification: Primary: 35K57, 37B40; Secondary: 92D3.
Citation: Dashun Xu, Xiao-Qiang Zhao. Asymptotic speed of spread and traveling waves for a nonlocal epidemic model. Discrete & Continuous Dynamical Systems - B, 2005, 5 (4) : 1043-1056. doi: 10.3934/dcdsb.2005.5.1043
[1]

Shuang-Ming Wang, Zhaosheng Feng, Zhi-Cheng Wang, Liang Zhang. Spreading speed and periodic traveling waves of a time periodic and diffusive SI epidemic model with demographic structure. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021145
[2]

Fei-Ying Yang, Yan Li, Wan-Tong Li, Zhi-Cheng Wang. Traveling waves in a nonlocal dispersal Kermack-McKendrick epidemic model. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1969-1993. doi: 10.3934/dcdsb.2013.18.1969
[3]

Jingdong Wei, Jiangbo Zhou, Wenxia Chen, Zaili Zhen, Lixin Tian. Traveling waves in a nonlocal dispersal epidemic model with spatio-temporal delay. Communications on Pure & Applied Analysis, 2020, 19 (5) : 2853-2886. doi: 10.3934/cpaa.2020125
[4]

Meng Zhao, Wan-Tong Li, Wenjie Ni. Spreading speed of a degenerate and cooperative epidemic model with free boundaries. Discrete & Continuous Dynamical Systems - B, 2020, 25 (3) : 981-999. doi: 10.3934/dcdsb.2019199
[5]

Manjun Ma, Xiao-Qiang Zhao. Monostable waves and spreading speed for a reaction-diffusion model with seasonal succession. Discrete & Continuous Dynamical Systems - B, 2016, 21 (2) : 591-606. doi: 10.3934/dcdsb.2016.21.591
[6]

Zhenguo Bai, Tingting Zhao. Spreading speed and traveling waves for a non-local delayed reaction-diffusion system without quasi-monotonicity. Discrete & Continuous Dynamical Systems - B, 2018, 23 (10) : 4063-4085. doi: 10.3934/dcdsb.2018126
[7]

Chang-Hong Wu. Spreading speed and traveling waves for a two-species weak competition system with free boundary. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2441-2455. doi: 10.3934/dcdsb.2013.18.2441
[8]

Chufen Wu, Peixuan Weng. Asymptotic speed of propagation and traveling wavefronts for a SIR epidemic model. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 867-892. doi: 10.3934/dcdsb.2011.15.867
[9]

Zhiting Xu. Traveling waves for a diffusive SEIR epidemic model. Communications on Pure & Applied Analysis, 2016, 15 (3) : 871-892. doi: 10.3934/cpaa.2016.15.871
[10]

Yan Li, Wan-Tong Li, Guo Lin. Traveling waves of a delayed diffusive SIR epidemic model. Communications on Pure & Applied Analysis, 2015, 14 (3) : 1001-1022. doi: 10.3934/cpaa.2015.14.1001
[11]

Jiamin Cao, Peixuan Weng. Single spreading speed and traveling wave solutions of a diffusive pioneer-climax model without cooperative property. Communications on Pure & Applied Analysis, 2017, 16 (4) : 1405-1426. doi: 10.3934/cpaa.2017067
[12]

Xiongxiong Bao, Wenxian Shen, Zhongwei Shen. Spreading speeds and traveling waves for space-time periodic nonlocal dispersal cooperative systems. Communications on Pure & Applied Analysis, 2019, 18 (1) : 361-396. doi: 10.3934/cpaa.2019019
[13]

Nar Rawal, Wenxian Shen, Aijun Zhang. Spreading speeds and traveling waves of nonlocal monostable equations in time and space periodic habitats. Discrete & Continuous Dynamical Systems, 2015, 35 (4) : 1609-1640. doi: 10.3934/dcds.2015.35.1609
[14]

Gary Bunting, Yihong Du, Krzysztof Krakowski. Spreading speed revisited: Analysis of a free boundary model. Networks & Heterogeneous Media, 2012, 7 (4) : 583-603. doi: 10.3934/nhm.2012.7.583
[15]

Zhiting Xu. Traveling waves in an SEIR epidemic model with the variable total population. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3723-3742. doi: 10.3934/dcdsb.2016118
[16]

Wan-Tong Li, Wen-Bing Xu, Li Zhang. Traveling waves and entire solutions for an epidemic model with asymmetric dispersal. Discrete & Continuous Dynamical Systems, 2017, 37 (5) : 2483-2512. doi: 10.3934/dcds.2017107
[17]

Jinling Zhou, Yu Yang, Cheng-Hsiung Hsu. Traveling waves for a nonlocal dispersal vaccination model with general incidence. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1469-1495. doi: 10.3934/dcdsb.2019236
[18]

Zigen Ouyang, Chunhua Ou. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 993-1007. doi: 10.3934/dcdsb.2012.17.993
[19]

Yang Yang, Yun-Rui Yang, Xin-Jun Jiao. Traveling waves for a nonlocal dispersal SIR model equipped delay and generalized incidence. Electronic Research Archive, 2020, 28 (1) : 1-13. doi: 10.3934/era.2020001
[20]

Yu-Xia Hao, Wan-Tong Li, Fei-Ying Yang. Traveling waves in a nonlocal dispersal predator-prey model. Discrete & Continuous Dynamical Systems - S, 2021, 14 (9) : 3113-3139. doi: 10.3934/dcdss.2020340

2020 Impact Factor: 1.327

Tools

Metrics

  • PDF downloads (85)
  • HTML views (0)
  • Cited by (24)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences | Privacy Policy