-
Previous Article
Analytical and numerical results on the positivity of steady state solutions of a thin film equation
- DCDS-B Home
- This Issue
-
Next Article
Finite-time quenching of competing species with constrained boundary evaporation
Traveling wave solutions for a diffusive sis epidemic model
| 1. | Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China |
| 2. | Department of Mathematical Science, University of Alabama in Huntsville, Huntsville, Alabama 35899, United States |
References:
| [1] |
L. J. S. Allen, B. M. Boller, Y. Lou and A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. A, 21 (2008), 1-20.
doi: 10.3934/dcds.2008.21.1. |
| [2] |
I. Beardmore and R. Beardmore, The global structure of a spatial model of infections disease, Proc. Roy. Soc. Lond. A., 459 (2003), 1427-1448.
doi: 10.1098/rspa.2002.1080. |
| [3] |
O. Diekmann, Thresholds and traveling waves for the geographical spread of infection, J. Math. Biol., 6 (1978), 109-130,
doi: 10.1007/BF02450783. |
| [4] |
O. Diekmann, Run for your life, A note on the aymptotic speed of propagation of an epidimic, J. Diff. Equations, 33 (1979), 58-73.
doi: 10.1016/0022-0396(79)90080-9. |
| [5] |
S. R. Dunbar, Traveling wave solutions of Diffusive Lotka-Volterra Equations: A heteroclinic connection in $\mathbbR^4$, Trans. Amer. Math. Society, 286 (1984), 557-594.
doi: 10.2307/1999810. |
| [6] |
P. C. Fife, "Mathematical Aspects of Reacting and Diffusing systems," Lecture Notes in Biomath, 28, Springer-Verlag, New York, 1979. |
| [7] |
W. Fitzgibbon, M. Langlais and J. J. Morgan, A mathematical model of the spread of Feline Leukemia Virus through a highly heterogeneous spatial domain, SIAM J. Math. Anal., 33 (2001), 570-588.
doi: 10.1137/S0036141000371757. |
| [8] |
W. Fitzgibbon, M. Langlais and J. J. Morgan, A reaction-diffusion system modelling direct and indirect transmission of diseases, Discrete and Continuous Dynamical Systems, Series B, 4 (2004), 893-910.
doi: 10.3934/dcdsb.2004.4.893. |
| [9] |
W. Fitzgibbon and M. Langlais, Simple models for the transmission of microparasites between host populations living on non coincident domains, Structured Population Models in Biology and Epidemiology Lecture Notes in Mathematics, 1936 (2008), 115-164. |
| [10] |
R. A. Gardner, Review on traveling wave solutions of parabolic systems by A. I. Volpert, V. A. Volpert, Bull. Aner. Math. Soc., 32 (1995), 446-452.
doi: 10.1090/S0273-0979-1995-00607-5. |
| [11] |
W. Huang, Traveling wave solutions for a class of predator-prey systems, Journal of Dynamics and Differential Equations, 24 (2012), 633-644.
doi: 10.1007/s10884-012-9255-4. |
| [12] |
W. Huang, M. Han and K. Liu, Dynamics of an SIS reaction-dissusion Epidemic Model for Disease transmission, Mathematical Biosciences and Engineering, 7 (2010), 51-66.
doi: 10.3934/mbe.2010.7.51. |
| [13] |
J. Keener and J. Sneyd, "Mathematical Physiology," Springer-Verlag, New York, Inc., 1998. |
| [14] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-I, Original Research Article Bulletin of Mathematical Biology, 53 (1991), 33-55. |
| [15] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-II. the problem of endemicity, Original Research Article Bulletin of Mathematical Biology, 53 (1991), 57-87. |
| [16] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-III. Further studies of the problem of endemicity, Original Research Article Bulletin of Mathematical Biology, 53 (1991), 89-118. |
| [17] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
| [18] |
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci, 196 (2005), 82-98.
doi: 10.1016/j.mbs.2005.03.008. |
| [19] |
X. Liang and X. Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure and Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
| [20] |
R. Peng and S. Liu, Global stability of the steady states of an SIS epidemic reaction-diffusion model, Non. Analysis, 71 (2009), 239-247.
doi: 10.1016/j.na.2008.10.043. |
| [21] |
J. Yang, S. Liang and Y. Zhang, Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion, PLoS ONE, 6 (2011), e21128.
doi: 10.1371/journal.pone.0021128. |
show all references
References:
| [1] |
L. J. S. Allen, B. M. Boller, Y. Lou and A. L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. A, 21 (2008), 1-20.
doi: 10.3934/dcds.2008.21.1. |
| [2] |
I. Beardmore and R. Beardmore, The global structure of a spatial model of infections disease, Proc. Roy. Soc. Lond. A., 459 (2003), 1427-1448.
doi: 10.1098/rspa.2002.1080. |
| [3] |
O. Diekmann, Thresholds and traveling waves for the geographical spread of infection, J. Math. Biol., 6 (1978), 109-130,
doi: 10.1007/BF02450783. |
| [4] |
O. Diekmann, Run for your life, A note on the aymptotic speed of propagation of an epidimic, J. Diff. Equations, 33 (1979), 58-73.
doi: 10.1016/0022-0396(79)90080-9. |
| [5] |
S. R. Dunbar, Traveling wave solutions of Diffusive Lotka-Volterra Equations: A heteroclinic connection in $\mathbbR^4$, Trans. Amer. Math. Society, 286 (1984), 557-594.
doi: 10.2307/1999810. |
| [6] |
P. C. Fife, "Mathematical Aspects of Reacting and Diffusing systems," Lecture Notes in Biomath, 28, Springer-Verlag, New York, 1979. |
| [7] |
W. Fitzgibbon, M. Langlais and J. J. Morgan, A mathematical model of the spread of Feline Leukemia Virus through a highly heterogeneous spatial domain, SIAM J. Math. Anal., 33 (2001), 570-588.
doi: 10.1137/S0036141000371757. |
| [8] |
W. Fitzgibbon, M. Langlais and J. J. Morgan, A reaction-diffusion system modelling direct and indirect transmission of diseases, Discrete and Continuous Dynamical Systems, Series B, 4 (2004), 893-910.
doi: 10.3934/dcdsb.2004.4.893. |
| [9] |
W. Fitzgibbon and M. Langlais, Simple models for the transmission of microparasites between host populations living on non coincident domains, Structured Population Models in Biology and Epidemiology Lecture Notes in Mathematics, 1936 (2008), 115-164. |
| [10] |
R. A. Gardner, Review on traveling wave solutions of parabolic systems by A. I. Volpert, V. A. Volpert, Bull. Aner. Math. Soc., 32 (1995), 446-452.
doi: 10.1090/S0273-0979-1995-00607-5. |
| [11] |
W. Huang, Traveling wave solutions for a class of predator-prey systems, Journal of Dynamics and Differential Equations, 24 (2012), 633-644.
doi: 10.1007/s10884-012-9255-4. |
| [12] |
W. Huang, M. Han and K. Liu, Dynamics of an SIS reaction-dissusion Epidemic Model for Disease transmission, Mathematical Biosciences and Engineering, 7 (2010), 51-66.
doi: 10.3934/mbe.2010.7.51. |
| [13] |
J. Keener and J. Sneyd, "Mathematical Physiology," Springer-Verlag, New York, Inc., 1998. |
| [14] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-I, Original Research Article Bulletin of Mathematical Biology, 53 (1991), 33-55. |
| [15] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-II. the problem of endemicity, Original Research Article Bulletin of Mathematical Biology, 53 (1991), 57-87. |
| [16] |
W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics-III. Further studies of the problem of endemicity, Original Research Article Bulletin of Mathematical Biology, 53 (1991), 89-118. |
| [17] |
M. A. Lewis, B. Li and H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233.
doi: 10.1007/s002850200144. |
| [18] |
B. Li, H. F. Weinberger and M. A. Lewis, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci, 196 (2005), 82-98.
doi: 10.1016/j.mbs.2005.03.008. |
| [19] |
X. Liang and X. Q. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure and Appl. Math., 60 (2007), 1-40.
doi: 10.1002/cpa.20154. |
| [20] |
R. Peng and S. Liu, Global stability of the steady states of an SIS epidemic reaction-diffusion model, Non. Analysis, 71 (2009), 239-247.
doi: 10.1016/j.na.2008.10.043. |
| [21] |
J. Yang, S. Liang and Y. Zhang, Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion, PLoS ONE, 6 (2011), e21128.
doi: 10.1371/journal.pone.0021128. |
| [1] |
Yoichi Enatsu, Emiko Ishiwata, Takeo Ushijima. Traveling wave solution for a diffusive simple epidemic model with a free boundary. Discrete and Continuous Dynamical Systems - S, 2021, 14 (3) : 835-850. doi: 10.3934/dcdss.2020387 |
| [2] |
Ran Zhang, Shengqiang Liu. On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 1197-1204. doi: 10.3934/dcdsb.2020159 |
| [3] |
Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, 2021, 29 (3) : 2325-2358. doi: 10.3934/era.2020118 |
| [4] |
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chang-Hong Wu. The sign of traveling wave speed in bistable dynamics. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3451-3466. doi: 10.3934/dcds.2020047 |
| [5] |
Jiamin Cao, Peixuan Weng. Single spreading speed and traveling wave solutions of a diffusive pioneer-climax model without cooperative property. Communications on Pure and Applied Analysis, 2017, 16 (4) : 1405-1426. doi: 10.3934/cpaa.2017067 |
| [6] |
Chufen Wu, Peixuan Weng. Asymptotic speed of propagation and traveling wavefronts for a SIR epidemic model. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 867-892. doi: 10.3934/dcdsb.2011.15.867 |
| [7] |
Dashun Xu, Xiao-Qiang Zhao. Asymptotic speed of spread and traveling waves for a nonlocal epidemic model. Discrete and Continuous Dynamical Systems - B, 2005, 5 (4) : 1043-1056. doi: 10.3934/dcdsb.2005.5.1043 |
| [8] |
Aiyong Chen, Chi Zhang, Wentao Huang. Limit speed of traveling wave solutions for the perturbed generalized KdV equation. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022048 |
| [9] |
Linghai Zhang. Wave speed analysis of traveling wave fronts in delayed synaptically coupled neuronal networks. Discrete and Continuous Dynamical Systems, 2014, 34 (5) : 2405-2450. doi: 10.3934/dcds.2014.34.2405 |
| [10] |
Wentao Meng, Yuanxi Yue, Manjun Ma. The minimal wave speed of the Lotka-Volterra competition model with seasonal succession. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021265 |
| [11] |
Jong-Shenq Guo, Ying-Chih Lin. Traveling wave solution for a lattice dynamical system with convolution type nonlinearity. Discrete and Continuous Dynamical Systems, 2012, 32 (1) : 101-124. doi: 10.3934/dcds.2012.32.101 |
| [12] |
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 and Applied Analysis, 2022, 21 (6) : 2005-2034. doi: 10.3934/cpaa.2021145 |
| [13] |
Jia-Bing Wang, Shao-Xia Qiao, Chufen Wu. Wave phenomena in a compartmental epidemic model with nonlocal dispersal and relapse. Discrete and Continuous Dynamical Systems - B, 2022, 27 (5) : 2635-2660. doi: 10.3934/dcdsb.2021152 |
| [14] |
M. B. A. Mansour. Computation of traveling wave fronts for a nonlinear diffusion-advection model. Mathematical Biosciences & Engineering, 2009, 6 (1) : 83-91. doi: 10.3934/mbe.2009.6.83 |
| [15] |
Zhaosheng Feng, Goong Chen. Traveling wave solutions in parametric forms for a diffusion model with a nonlinear rate of growth. Discrete and Continuous Dynamical Systems, 2009, 24 (3) : 763-780. doi: 10.3934/dcds.2009.24.763 |
| [16] |
Junhao Wen, Peixuan Weng. Traveling wave solutions in a diffusive producer-scrounger model. Discrete and Continuous Dynamical Systems - B, 2017, 22 (2) : 627-645. doi: 10.3934/dcdsb.2017030 |
| [17] |
Jiang Liu, Xiaohui Shang, Zengji Du. Traveling wave solutions of a reaction-diffusion predator-prey model. Discrete and Continuous Dynamical Systems - S, 2017, 10 (5) : 1063-1078. doi: 10.3934/dcdss.2017057 |
| [18] |
Liang Zhang, Bingtuan Li. Traveling wave solutions in an integro-differential competition model. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 417-428. doi: 10.3934/dcdsb.2012.17.417 |
| [19] |
Vincent Calvez, Benoȋt Perthame, Shugo Yasuda. Traveling wave and aggregation in a flux-limited Keller-Segel model. Kinetic and Related Models, 2018, 11 (4) : 891-909. doi: 10.3934/krm.2018035 |
| [20] |
Bang-Sheng Han, Zhi-Cheng Wang. Traveling wave solutions in a nonlocal reaction-diffusion population model. Communications on Pure and Applied Analysis, 2016, 15 (3) : 1057-1076. doi: 10.3934/cpaa.2016.15.1057 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]