[1] |
HARRIS T E. Contact interactions on a lattice[J]. Ann Probab, 1974, 2(6): 969-988.
|
[2] |
LIGGETT T M. Interacting Particle Systems[M]. New York: Springer,1985.
|
[3] |
LIGGETT T M. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes[M]. New York: Springer,1999.
|
[4] |
SUDBURY A. Rigorous lower bounds for the critical infection rate in the diffusive contact process[J]. J Appl Probab, 2001, 38(4): 1074-1078.
|
[5] |
纪瑞瑞. 一维单边接触过程性质的研究[D]. 芜湖:安徽师范大学,2010.
|
[6] |
李建全, 娄洁, 娄梅枝. 离散的SI 和SIS 传染病模型的研究[J]. 应用数学和力学,2008, 29(1):104-110. LI Jianquan, LOU Jie,LOU Meizhi.Study of some discrete SI and SIS epidemic models[J].Applied Mathematics and Mechanics,2008, 29(1):104-110.
|
[7] |
PEMANTLE R. The contact process on trees[J]. Ann Probab, 1992, 20(4): 2089-2116.
|
[8] |
ZHANG Y. The complete convergence theorem of the contact process on trees[J]. The Annals of Probability, 1996, 24: 1408-1443.
|
[9] |
SALZANO M,SCHONMANN R H. A new proof that for the contact process on homogeneous trees local survival implies complete convergence[J]. The Annals of Probability, 1998, 26: 1251-1258.
|
[10] |
曹宇. 传染病动力学模型研究[D]. 沈阳:东北大学,2014.
|
[11] |
XUE X. An improved upper bound for the critical value of the contact process on Zd with d≥3[J]. Electron Commun Probab, 2018,23: No.77.
|
[12] |
CRANSTON M, MOUNTFORD T,MOURRAT J C, et al. The contact process on finite homogeneous trees revisited[J]. ALEA Lat Am J Probab Math Stat, 2014, 11: 385-408.
|
[13] |
张刚强. 关于基本接触过程临界值的新估计[J]. 华中理工大学学报,1999,27(6):94-96.ZHANG Gangqiang. Estimation of the critical value in the basic contact process[J]. J Huazhong Univ of Sci & Tech,1999,27(6):94-96.
|
[14] |
丁万鼎, 朱作宾. 基本接触过程临界值的新估计[J]. 安徽师范大学学报(自然科学版),1984(1):3-8.
|
[15] |
AIZENMAN M, JUNG P. On the critical behavior at the lower phase transition of the contact process[J]. ALEA Lat Am J Probab Math Stat, 2007, 3: 301-320.
|
[16] |
PETERSON J. The contact process on the complete graph with random vertex-dependent infection rates[J]. Stochastic Processes and Their Applications, 2011, 121: 609-629.
|
[17] |
ARMBRUSTER B, BECK E. Elementary proof of convergence to the mean-field model for the SIR process[J]. J Math Biol,2017,75:327-339.
|
[18] |
王高雄, 周之铭,朱思铭,等. 常微分方程[M]. 第3 版. 北京: 高等教育出版社, 2006: 219.
|
[19] |
PASTOR-SATORRAS R, VESPIGNANI A. Epidemic spreading in scale-free networks[J]. Physical Review Letters, 2001, 86: 3200-3203.
|
[20] |
PASTOR-SATORRAS R, VESPIGNANI A. Epidemic dynamics and endemic states in complex networks[J]. Physical Review E, 2001, 63: 066117.
|
[21] |
李彦. 复杂网络上的相变问题研究[D]. 上海:上海交通大学,2014.
|
[22] |
XUE X. Priority of the result in “Mean field limit for survival probability of the high-dimensional contact process”[J]. Statist Probab Lett, 2019, 148: 133.
|
[23] |
KURTZ T G. Strong approximation theorems for density dependent Markov chains[J]. Stochastic Processes and Their Applications, 1978, 6: 223-240.
|
[24] |
张恭庆, 郭懋正. 泛函分析讲义(下册)[M]. 北京: 北京大学出版社, 1990: 45-130.)
|
[1] |
HARRIS T E. Contact interactions on a lattice[J]. Ann Probab, 1974, 2(6): 969-988.
|
[2] |
LIGGETT T M. Interacting Particle Systems[M]. New York: Springer,1985.
|
[3] |
LIGGETT T M. Stochastic Interacting Systems: Contact, Voter and Exclusion Processes[M]. New York: Springer,1999.
|
[4] |
SUDBURY A. Rigorous lower bounds for the critical infection rate in the diffusive contact process[J]. J Appl Probab, 2001, 38(4): 1074-1078.
|
[5] |
纪瑞瑞. 一维单边接触过程性质的研究[D]. 芜湖:安徽师范大学,2010.
|
[6] |
李建全, 娄洁, 娄梅枝. 离散的SI 和SIS 传染病模型的研究[J]. 应用数学和力学,2008, 29(1):104-110. LI Jianquan, LOU Jie,LOU Meizhi.Study of some discrete SI and SIS epidemic models[J].Applied Mathematics and Mechanics,2008, 29(1):104-110.
|
[7] |
PEMANTLE R. The contact process on trees[J]. Ann Probab, 1992, 20(4): 2089-2116.
|
[8] |
ZHANG Y. The complete convergence theorem of the contact process on trees[J]. The Annals of Probability, 1996, 24: 1408-1443.
|
[9] |
SALZANO M,SCHONMANN R H. A new proof that for the contact process on homogeneous trees local survival implies complete convergence[J]. The Annals of Probability, 1998, 26: 1251-1258.
|
[10] |
曹宇. 传染病动力学模型研究[D]. 沈阳:东北大学,2014.
|
[11] |
XUE X. An improved upper bound for the critical value of the contact process on Zd with d≥3[J]. Electron Commun Probab, 2018,23: No.77.
|
[12] |
CRANSTON M, MOUNTFORD T,MOURRAT J C, et al. The contact process on finite homogeneous trees revisited[J]. ALEA Lat Am J Probab Math Stat, 2014, 11: 385-408.
|
[13] |
张刚强. 关于基本接触过程临界值的新估计[J]. 华中理工大学学报,1999,27(6):94-96.ZHANG Gangqiang. Estimation of the critical value in the basic contact process[J]. J Huazhong Univ of Sci & Tech,1999,27(6):94-96.
|
[14] |
丁万鼎, 朱作宾. 基本接触过程临界值的新估计[J]. 安徽师范大学学报(自然科学版),1984(1):3-8.
|
[15] |
AIZENMAN M, JUNG P. On the critical behavior at the lower phase transition of the contact process[J]. ALEA Lat Am J Probab Math Stat, 2007, 3: 301-320.
|
[16] |
PETERSON J. The contact process on the complete graph with random vertex-dependent infection rates[J]. Stochastic Processes and Their Applications, 2011, 121: 609-629.
|
[17] |
ARMBRUSTER B, BECK E. Elementary proof of convergence to the mean-field model for the SIR process[J]. J Math Biol,2017,75:327-339.
|
[18] |
王高雄, 周之铭,朱思铭,等. 常微分方程[M]. 第3 版. 北京: 高等教育出版社, 2006: 219.
|
[19] |
PASTOR-SATORRAS R, VESPIGNANI A. Epidemic spreading in scale-free networks[J]. Physical Review Letters, 2001, 86: 3200-3203.
|
[20] |
PASTOR-SATORRAS R, VESPIGNANI A. Epidemic dynamics and endemic states in complex networks[J]. Physical Review E, 2001, 63: 066117.
|
[21] |
李彦. 复杂网络上的相变问题研究[D]. 上海:上海交通大学,2014.
|
[22] |
XUE X. Priority of the result in “Mean field limit for survival probability of the high-dimensional contact process”[J]. Statist Probab Lett, 2019, 148: 133.
|
[23] |
KURTZ T G. Strong approximation theorems for density dependent Markov chains[J]. Stochastic Processes and Their Applications, 1978, 6: 223-240.
|
[24] |
张恭庆, 郭懋正. 泛函分析讲义(下册)[M]. 北京: 北京大学出版社, 1990: 45-130.)
|