Computer Science ›› 2016, Vol. 43 ›› Issue (Z6): 64-67.doi: 10.11896/j.issn.1002-137X.2016.6A.014

Previous Articles     Next Articles

SIRS Epidemic Model and its Threshold Based on State Transition Probability

GU Hai-jun, JIANG Guo-ping and XIA Ling-ling   

  • Online:2018-12-01 Published:2018-12-01

Abstract: For SIRS (Susceptible-Infected-Removed-Susceptible) epidemic model,we used the method of state transition probability to study the SIRS epidemic process through calculating the probability in each state over time.First,we established state probability equations to describe the probability in susceptible state,infection state and immune state of each node at each moment.Then,we derived the epidemic threshold of SIRS model by the theory of steady state analysis.Finally,using the Monte Carlo method,we analyzed and simulated the epidemic threshold in both homogeneous network and heterogeneous network.Compared with the traditional mean-field method,the simulation results show that the threshold obtained by the state probability equations is much closer to real Monte Carlo value and has no relations with the immune deficiency rate.

Key words: Epidemic threshold,Probability equations,SIRS model,Mean-field method

[1] Zhou Tao,Liu Jian-guo,Bai Wen-jie,et al.Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity[J].Physical Review E,2006,74(5):056109
[2] Shi Hong-jing,Duan Zhi-sheng,Chen Guang-rong.An SIS model with infective medium on complex networks[J].Physica A:Statistical Mechanics and its Applications,2008,387(8):2133-2144
[3] Wang Jia-zeng,Liu Zeng-rong,Xu Jian-hua.Epidemic spreading on uncorrelated heterogenous networks with non-uniform transmission[J].Physica A:Statistical Mechanics and its Applications,2007,382(2):715-721
[4] Da Silva R,Fernandes H A.A study of the influence of the mobility on the phase transitions of the synchronous SIR model[J].Journal of Statistical Mechanics:Theory and Experiment,2015,5(6):P06011
[5] 马之恩,周义仓,王稳地.传染病动力学的数学建模与研究[M].北京:科学出版社,2004
[6] 巩永旺.考虑个体行为的复杂网络病毒传播研究[D].南京:南京邮电大学,2014
[7] 侯鹏锋,赵海兴.一种星-树结构的确定性的小世界网络[J].计算机科学与应用,2014(4):276-281
[8] 胡耀光,王圣军,金涛,等.度关联无标度网络上的有倾向随机行走[J].物理学报,2015,4(2):028901-028901
[9] 王亚奇,蒋国平.复杂网络中考虑不完全免疫的病毒传播研究[J].物理学报,2010,59(10):6734-6743
[10] Pastor-Satorras R,Vespignani A.Epidemic dynamics and endemic states in complex networks[J].Physical Review E,2001,63(6):066117
[11] Pastor-Satorras R,Vespignani A.Epidemic spreading in scale-free networks[J].Physical review letters,2001,86(14):3200-3203
[12] May R M,Lloyd A L.Infection dynamics on scale-free networks[J].Physical Review E,2001,64(6):066112
[13] Yang Rui,Wang Bing-hong,Ren Jie,et al.Epidemic spreading on heterogeneous networks with identical infectivity[J].Physics Letters A,2007,364(3):189-193
[14] Moore C,Newman M E J.Epidemics and percolation in small-world networks[J].Physical Review E,2000,61(5):5678
[15] Stone T,McKay S.Critical behavior of disease spread on dyna-mic small-world networks [J].Europhysics Letters,2011,5(3):38003
[16] Boguá M,Pastor-Satorras R,Vespignani A.Absence of epi-demic threshold in scale-free networks with degree correlations[J].Physical review letters,2003,90(2):028701
[17] Chakrabarti D,Wang Y,Wang C,et al.Epidemic thresholds in real networks[J].ACM Transactions on Information and System Security (TISSEC),2008,10(4):1
[18] Moreno Y,Gómez J B,Pacheco A F.Epidemic incidence in correlated complex networks[J].Physical Review E,2003,68(3):035103
[19] Barthélemy M,Barrat A,Pastor-Satorras R,et al.Velocity and hierarchical spread of epidemic outbreaks in scale-free networks[J].Physical Review Letters,2004,92(17):178701
[20] Guerra B,Gómez-Gardees J.Annealed and mean-field formulations of disease dynamics on static and adaptive networks[J].Physical Review E,2010,82(3):035101
[21] Smilkov D,Kocarev L.Influence of the network topology on epidemic spreading[J].Physical Review E,2012,85(1):016114
[22] Eslahchi C,Movahedi F.Calculation of transition probabilities in the birth and death Markov process in the epidemic model[J].Mathematical and Computer Modelling,2012,55(3):810-815
[23] Trpevski D,Tang W K S,Kocarev L.Model for rumor spreading over networks[J].Physical Review E,2010,81(5):056102
[24] 李光正,史定华.复杂网络上SIRS类疾病传播行为分析[J].自然科学进展,2006,16(4):508-512

No related articles found!
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] LEI Li-hui and WANG Jing. Parallelization of LTL Model Checking Based on Possibility Measure[J]. Computer Science, 2018, 45(4): 71 -75, 88 .
[2] XIA Qing-xun and ZHUANG Yi. Remote Attestation Mechanism Based on Locality Principle[J]. Computer Science, 2018, 45(4): 148 -151, 162 .
[3] LI Bai-shen, LI Ling-zhi, SUN Yong and ZHU Yan-qin. Intranet Defense Algorithm Based on Pseudo Boosting Decision Tree[J]. Computer Science, 2018, 45(4): 157 -162 .
[4] WANG Huan, ZHANG Yun-feng and ZHANG Yan. Rapid Decision Method for Repairing Sequence Based on CFDs[J]. Computer Science, 2018, 45(3): 311 -316 .
[5] SUN Qi, JIN Yan, HE Kun and XU Ling-xuan. Hybrid Evolutionary Algorithm for Solving Mixed Capacitated General Routing Problem[J]. Computer Science, 2018, 45(4): 76 -82 .
[6] ZHANG Jia-nan and XIAO Ming-yu. Approximation Algorithm for Weighted Mixed Domination Problem[J]. Computer Science, 2018, 45(4): 83 -88 .
[7] WU Jian-hui, HUANG Zhong-xiang, LI Wu, WU Jian-hui, PENG Xin and ZHANG Sheng. Robustness Optimization of Sequence Decision in Urban Road Construction[J]. Computer Science, 2018, 45(4): 89 -93 .
[8] LIU Qin. Study on Data Quality Based on Constraint in Computer Forensics[J]. Computer Science, 2018, 45(4): 169 -172 .
[9] ZHONG Fei and YANG Bin. License Plate Detection Based on Principal Component Analysis Network[J]. Computer Science, 2018, 45(3): 268 -273 .
[10] SHI Wen-jun, WU Ji-gang and LUO Yu-chun. Fast and Efficient Scheduling Algorithms for Mobile Cloud Offloading[J]. Computer Science, 2018, 45(4): 94 -99, 116 .