-
Previous Article
A nonlocal and fully nonlinear degenerate parabolic system from strain-gradient plasticity
- DCDS-B Home
- This Issue
- Next Article
Threshold dynamics of a bacillary dysentery model with seasonal fluctuation
1. | Department of Mathematics, Xi’an Jiaotong University, Xi’an, 710049, China |
References:
[1] |
, The Facts about shigella infections and bacillary dysentery, Association of Medical Microbiologists, http://www.amm.co.uk/files/factsabout/fa_shig.htm. |
[2] |
, Disease Control and Public Health,, China's Health Statistical Yearbook 2009, (2009).
|
[3] |
, Main Population Data in 2008, China, China Population and Development Research Center, http://www.cpirc.org.cn/en-cpdrc/en-file/endata/en-data-10.html. |
[4] |
, Birth rate, Death Rate and Natural Growth Rate of Population,, China Statistical Yearbook 2008, (2008).
|
[5] |
, Population and Its Composition,, China Statistical Yearbook 2008, (2008).
|
[6] |
, http://baike.baidu.com/view/1161053.htm, http://baike.baidu.com/view/1161053.htm. |
[7] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Academic Press, Boston, 1993. |
[8] |
V. Lakshmikantham, S. Leela and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Marcell Dekker, Inc., New York, Basel, 1989. |
[9] |
L. Liu, X. -Q. Zhao and Y. Zhou, A tuberculosis model with seasonality, Bulletin of Mathematical Biology, 72 (2010), 931-952.
doi: doi:10.1007/s11538-009-9477-8. |
[10] |
, National report of notifiable diseases, 2005-2008, Ministry of Health of the People's Republic of China, http://www.moh.gov.cn/publicfiles//business/htmlfiles/zwgkzt/pyq/list.htm. |
[11] |
Z. Teng and L. Chen, The positive periodic solutions for high dimensional periodic Kolmogorov-type systems with delays, Acta Mathematicae Applicatae Sinica (Chinese Series), 22 (1999), 446-456. |
[12] |
X. Wang, F. Tao, D. Xiao, Lee H, Deen J, Gong J, et al., Trend and disease burden of bacillary dysentery in China (1991-2000), Bull World Health Organ., 84 (2006), 561-568. |
[13] |
W. Wang, X. -Q. Zhao, Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments, J. Dyn. Diff. Equat., 20 (2008), 699-717. |
[14] |
X. -Q. Zhao, "Dynamical Systems in Population Biology," Springer-Verlag, New York, 2003. |
show all references
References:
[1] |
, The Facts about shigella infections and bacillary dysentery, Association of Medical Microbiologists, http://www.amm.co.uk/files/factsabout/fa_shig.htm. |
[2] |
, Disease Control and Public Health,, China's Health Statistical Yearbook 2009, (2009).
|
[3] |
, Main Population Data in 2008, China, China Population and Development Research Center, http://www.cpirc.org.cn/en-cpdrc/en-file/endata/en-data-10.html. |
[4] |
, Birth rate, Death Rate and Natural Growth Rate of Population,, China Statistical Yearbook 2008, (2008).
|
[5] |
, Population and Its Composition,, China Statistical Yearbook 2008, (2008).
|
[6] |
, http://baike.baidu.com/view/1161053.htm, http://baike.baidu.com/view/1161053.htm. |
[7] |
Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," Academic Press, Boston, 1993. |
[8] |
V. Lakshmikantham, S. Leela and A. A. Martynyuk, "Stability Analysis of Nonlinear Systems," Marcell Dekker, Inc., New York, Basel, 1989. |
[9] |
L. Liu, X. -Q. Zhao and Y. Zhou, A tuberculosis model with seasonality, Bulletin of Mathematical Biology, 72 (2010), 931-952.
doi: doi:10.1007/s11538-009-9477-8. |
[10] |
, National report of notifiable diseases, 2005-2008, Ministry of Health of the People's Republic of China, http://www.moh.gov.cn/publicfiles//business/htmlfiles/zwgkzt/pyq/list.htm. |
[11] |
Z. Teng and L. Chen, The positive periodic solutions for high dimensional periodic Kolmogorov-type systems with delays, Acta Mathematicae Applicatae Sinica (Chinese Series), 22 (1999), 446-456. |
[12] |
X. Wang, F. Tao, D. Xiao, Lee H, Deen J, Gong J, et al., Trend and disease burden of bacillary dysentery in China (1991-2000), Bull World Health Organ., 84 (2006), 561-568. |
[13] |
W. Wang, X. -Q. Zhao, Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments, J. Dyn. Diff. Equat., 20 (2008), 699-717. |
[14] |
X. -Q. Zhao, "Dynamical Systems in Population Biology," Springer-Verlag, New York, 2003. |
[1] |
Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377-393. doi: 10.3934/mbe.2009.6.377 |
[2] |
Hui Cao, Yicang Zhou. The basic reproduction number of discrete SIR and SEIS models with periodic parameters. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 37-56. doi: 10.3934/dcdsb.2013.18.37 |
[3] |
Ariel Cintrón-Arias, Carlos Castillo-Chávez, Luís M. A. Bettencourt, Alun L. Lloyd, H. T. Banks. The estimation of the effective reproductive number from disease outbreak data. Mathematical Biosciences & Engineering, 2009, 6 (2) : 261-282. doi: 10.3934/mbe.2009.6.261 |
[4] |
Dominika Pilarczyk. Asymptotic stability of singular solution to nonlinear heat equation. Discrete and Continuous Dynamical Systems, 2009, 25 (3) : 991-1001. doi: 10.3934/dcds.2009.25.991 |
[5] |
Lakmi Niwanthi Wadippuli, Ivan Gudoshnikov, Oleg Makarenkov. Global asymptotic stability of nonconvex sweeping processes. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 1129-1139. doi: 10.3934/dcdsb.2019212 |
[6] |
Christian Lax, Sebastian Walcher. A note on global asymptotic stability of nonautonomous master equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (8) : 2143-2149. doi: 10.3934/dcdsb.2013.18.2143 |
[7] |
Rafael Luís, Sandra Mendonça. A note on global stability in the periodic logistic map. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4211-4220. doi: 10.3934/dcdsb.2020094 |
[8] |
Mi-Young Kim. Uniqueness and stability of positive periodic numerical solution of an epidemic model. Discrete and Continuous Dynamical Systems - B, 2007, 7 (2) : 365-375. doi: 10.3934/dcdsb.2007.7.365 |
[9] |
Qiang Li, Mei Wei. Existence and asymptotic stability of periodic solutions for neutral evolution equations with delay. Evolution Equations and Control Theory, 2020, 9 (3) : 753-772. doi: 10.3934/eect.2020032 |
[10] |
Kentarou Fujie. Global asymptotic stability in a chemotaxis-growth model for tumor invasion. Discrete and Continuous Dynamical Systems - S, 2020, 13 (2) : 203-209. doi: 10.3934/dcdss.2020011 |
[11] |
Fabien Crauste. Global Asymptotic Stability and Hopf Bifurcation for a Blood Cell Production Model. Mathematical Biosciences & Engineering, 2006, 3 (2) : 325-346. doi: 10.3934/mbe.2006.3.325 |
[12] |
Shiwang Ma, Xiao-Qiang Zhao. Global asymptotic stability of minimal fronts in monostable lattice equations. Discrete and Continuous Dynamical Systems, 2008, 21 (1) : 259-275. doi: 10.3934/dcds.2008.21.259 |
[13] |
Anatoli F. Ivanov, Musa A. Mammadov. Global asymptotic stability in a class of nonlinear differential delay equations. Conference Publications, 2011, 2011 (Special) : 727-736. doi: 10.3934/proc.2011.2011.727 |
[14] |
Tianhui Yang, Lei Zhang. Remarks on basic reproduction ratios for periodic abstract functional differential equations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (12) : 6771-6782. doi: 10.3934/dcdsb.2019166 |
[15] |
Dongfeng Zhang, Junxiang Xu. On the reducibility of analytic quasi-periodic systems with Liouvillean basic frequencies. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1417-1445. doi: 10.3934/cpaa.2022024 |
[16] |
Zigen Ouyang, Chunhua Ou. Global stability and convergence rate of traveling waves for a nonlocal model in periodic media. Discrete and Continuous Dynamical Systems - B, 2012, 17 (3) : 993-1007. doi: 10.3934/dcdsb.2012.17.993 |
[17] |
Nicolas Bacaër, Xamxinur Abdurahman, Jianli Ye, Pierre Auger. On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China. Mathematical Biosciences & Engineering, 2007, 4 (4) : 595-607. doi: 10.3934/mbe.2007.4.595 |
[18] |
Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2021170 |
[19] |
Zhijun Zhang. Optimal global asymptotic behavior of the solution to a singular monge-ampère equation. Communications on Pure and Applied Analysis, 2020, 19 (2) : 1129-1145. doi: 10.3934/cpaa.2020053 |
[20] |
Jing Li, Boling Guo, Lan Zeng, Yitong Pei. Global weak solution and smooth solution of the periodic initial value problem for the generalized Landau-Lifshitz-Bloch equation in high dimensions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (4) : 1345-1360. doi: 10.3934/dcdsb.2019230 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]