Skip to main content
Download PDF

Mathematical and computational approaches to epidemic modeling: a comprehensive review

Frontiers of Computer Science volume 9, pages 806–826 (2015)Cite this article

Abstract

Mathematical and computational approaches are important tools for understanding epidemic spread patterns and evaluating policies of disease control. In recent years, epidemiology has become increasingly integrated with mathematics, sociology, management science, complexity science, and computer science. The cross of multiple disciplines has caused rapid development of mathematical and computational approaches to epidemic modeling. In this article, we carry out a comprehensive review of epidemic models to provide an insight into the literature of epidemic modeling and simulation. We introduce major epidemic models in three directions, including mathematical models, complex network models, and agent-based models. We discuss the principles, applications, advantages, and limitations of these models. Meanwhile, we also propose some future research directions in epidemic modeling.

References

  1. Grassly N C, Fraser C. Mathematical models of infectious disease transmission. Nature, 2008, 6(6): 477–487

    Google Scholar 

  2. Epstein J M, Parker J, Cummings D, Hammond A. Coupled contagion dynamics of fear and disease: mathematical and computational explorations. PLoS ONE, 2008, 3(12): e3955

    Article  Google Scholar 

  3. Ajelli M, Goncalves B, Balcan D, Colizza V, Hu H, Ramasco J J, Merler S, Vespignani A. Comparing large-scale computational approaches to epidemic modeling: agent-based versus structure metapopulation models. BMC Infectious Diseases, 2010, 10(190): 1–13

    Google Scholar 

  4. Brown S T, Tai J H Y, Bailey R R, Cooley P C, Wheaton W D, Potter M A, Voorhees R E, LeJeune M, Grefenstette J J, Burke D S, McGlone S M, Lee B Y. Would school closure for the 2009 H1N1 influenza epidemic have been worth the cost: a computational simulation of Pennsylvania. BMC Public Health, 2011, 11(353): 1–11

    Google Scholar 

  5. Nsoesie E O, Beckman R J, Shashaani S, Nagaraj K S, Marathe M V. A simulation optimization approach to epidemic forecasting. PLoS ONE, 2013, 8(6): e67164

    Article  Google Scholar 

  6. Burke D S, Epstein J M, Cummings D A, Parker J I, Cline K C, Singa R M, Chakravarty S. Individual-based computational modeling of smallpox epidemic control strategies. Academic Emergency Medicine, 2006, 13(11): 1142–1149

    Article  Google Scholar 

  7. Kretzschmar M, Wallinga J. Mathematical models in infections Disease. In: Krämer A, Kretzschmar M, Krickeberg K, eds. Modern infectious disease epidemiology, statistic for biology and health. Springer Science+Business Media, LLC, 2010: 209–221

    Google Scholar 

  8. Fournié G, Walker P, Porphyre T, Métras R, Pfeiffer D. Health and animal agriculture in developing countries, natural resource management and policy. Food and Agriculture Organization of the United Nations, 2012: 183–205

    Google Scholar 

  9. Abbey H. An examination of the Reed-Frost theory of epidemics. Human Biology, 1952, 24(3): 201–233

    Google Scholar 

  10. Maia J O C DE. Some mathematical developments on the epidemic theory formulated by Reed and Frost. Human Biology, 1952, 24(3): 167–200

    MathSciNet  Google Scholar 

  11. Kermack WO and McKendrick A G. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London (Series A), 1927, 115(772): 700–721

    MATH  Article  Google Scholar 

  12. Siettos C I, Russo L. Mathematical modeling of infectious disease dynamics. Virulence, 2013, 4(4): 295–306

    Article  Google Scholar 

  13. Dimitrov N B, Meyers L A. Mathematical approaches to infectious disease prediction and control. J. J. Hasenbein, ed. INFORMS Tutorials in Operations Research. 2010, 1–25

    Google Scholar 

  14. Keeling M J, Danon L. Mathematical modeling of infectious disease. British Medical Bulletin, 2009, 92(1): 33–42

    Article  Google Scholar 

  15. Garnett G P, Cousens S, Hallett T B, Steketee R, Walker N. Mathematical models in the evaluation of health programmes. Lancet, 2011, 378(9790): 515–525

    Article  Google Scholar 

  16. Britton T. Stochastic epidemic models: a survey. Mathematical Biosciences, 2010, 225(1): 24–35

    MathSciNet  MATH  Article  Google Scholar 

  17. Keeling M J, Rohani P. Modeling Infectious Diseases in Humans and Animals. Princeton: Princeton University Press, 2007

    Google Scholar 

  18. O’Neill P D. A tutorial introduction to Bayesian inference for stochastic epidemic models using Markov chain Monte Carlo methods. Mathematical Bioscience, 2002, 180(1–2): 103–114

    MathSciNet  MATH  Article  Google Scholar 

  19. Korostil I A, Peters G W, Cornebise J, Regan D G. Adaptive Markov Chain Monte Carlo forward projection for statistical analysis in epidemic modelling of human papillomavirus. Statistics in Medicine, 2013, 32(11): 1917–1953

    MathSciNet  Article  Google Scholar 

  20. Rorres C, Pelletier S T K, Smith G. Stochastic modeling of animal epidemics using data collected over three different spatial scales. Epidemics, 2011, 3(2): 61–70

    Article  Google Scholar 

  21. Forgoston E, Billings L, Schwartz I B. Accurate noise projection for reduced stochastic epidemic models. Chaos, 2009, 19(4): 043110

    MathSciNet  Article  Google Scholar 

  22. Schewartz I B, Billings L, Bollt E M. Dynamical epidemic suppression using stochastic prediction and control. Physical Review E, 2005, 70(4): 046220

    Article  Google Scholar 

  23. Schewartz I B, Billings L, Dykman M, Landsman A. Predicting extinction rates in stochastic epidemic models. Journal of Statistical Mechanics: Theory and Experiment, 2009, 2009(1): 01005

    Article  Google Scholar 

  24. Eseghir A, Kissami A, Maroufy H E, Ziad T. A branching process approximation of the final size of multitype collective Reed-Frost model. Journal of Statistics Application & Probability, 2013, 2(1): 47–59

    Article  Google Scholar 

  25. Neal P. Multitype randomized Reed-Frost epidemics and epidemics upon random graphs. The Annals of Applied Probability, 2006, 16(3): 1166–1189

    MathSciNet  MATH  Article  Google Scholar 

  26. O’Neill P D. Perfect simulation for Reed-Frost epidemic models. Statistics and Computing, 2003, 13(1): 37–44

    MathSciNet  Article  Google Scholar 

  27. Jacquez J A. A note on chain-binomial models of epidemic spread: what is wrong with the Reed-Frost formulation? Mathematical Bioscience, 1987, 87(1): 73–82

    MathSciNet  MATH  Article  Google Scholar 

  28. Kendall D G. Deterministic and stochastic epidemics in closed population. In: Proceedings of the Berkeley Symposium on Mathematical Statistics and Probability. 1956: 149–165

    Google Scholar 

  29. Allen L J S, Burgin A M. Comparison of deterministic and stochastic SIS and SIR models in discrete time. Mathematical Bioscience, 2000, 163(1): 1–33

    MathSciNet  MATH  Article  Google Scholar 

  30. Billings L, Spears W M, Schwartz I B. A unified prediction of computer virus spread in connected networks. Physics Letters A, 2002, 297(3): 261–266

    MathSciNet  MATH  Article  Google Scholar 

  31. West R W, Thompson J R. Models for the simple epidemic. Mathematical Bioscience, 1997, 141(1): 29–39

    MATH  Article  Google Scholar 

  32. Kwok K O, Leung G M, Lam W Y, Riley S. Using models to identify routes of nosocomial infection: a large hospital outbreak of SARS in Hong Kong. Proceedings of the Royal Society B, 2007, 274(1610): 611–617

    Article  Google Scholar 

  33. Mkhatshwa T, Mummert A. Modeling super-spreading events for infectious disease: case study SARS. IAENG International Journal of Applied Mathematics, 2011, 41(2): 82

    Google Scholar 

  34. Chowell G, Viboud C, Wang X, Bertozzi S M, Miler M A. Adaptive vaccination strategies to mitigate pandemic influenza: Mexico as a case study. PLoS ONE, 2009, 4(12): e8164.

    Article  Google Scholar 

  35. Zhang J, Lou J, Ma Z, Wu J. A compartmental model for the analysis of SARS transmission patterns and outbreak control measures in China. Applied Mathematics and Computation, 2005, 162(2): 909–924

    MATH  Article  Google Scholar 

  36. Ohkusa Y, Taniguchi K, Okubo I. Prediction of smallpox outbreak and evaluation of control-measure policy in Japan, using a mathematical model. Journal of Infection and Chemotherapy, 2005, 11(2): 71–80

    Article  Google Scholar 

  37. Fenichel E P, Castillo-Chavez C, Ceddia M G, Chowell G, Parra P A G, Hickling G J, Holloway G, Horan R, Morin B, Perrings C, Springborn M, Velazquez L, Villalobos C. Adaptive human behavior in epidemiological models. Proceedings of National Academy of Sciences USA, 2011, 108(15): 6306–6311

    Article  Google Scholar 

  38. Li Y, Yu I T, Xu P, Lee J H W, Wong T W, Ooi P L, Sleigh A C. Predicting Super Spreading Events during the 2003 Severe Acute Respiratory Syndrome Epidemics in Hong Kong and Singapore. American Journal of Epidemiology, 2004, 160(8): 719–728

    Article  Google Scholar 

  39. Eubank S, Guclu H, Kumar A, Marathe M V, Srinivasan A, Toroczkai Z, Wang N. Modeling disease outbreaks in realistic urban social networks. Nature, 2004, 429(6988): 180–184

    Article  Google Scholar 

  40. Kuperman M N. Invited review: epidemics on social networks. Paper in Physics, 2013, 5: 050003.

    Article  Google Scholar 

  41. Leskovec J, Krause A, Guestrin C, Faloutsos C, VanBriesen J, Glance N. Cost-effective outbreak detection in networks. In: Proceedings of the 13th ACM SIGKDD International conference on Knowledge discovery and data mining. 2007: 420–429

    Chapter  Google Scholar 

  42. Brouqui P, Puro V, Fusco F M, Bannister B, Schilling S, Follin P, Gottschalk R, Hemmer R, Maltezou H C, Ott K, Peleman R, Perronne C, Sheehan C, Siikamäki H, Skinhoj P, Ippolito G, EUNID Working Group. Infection control in the management of highly pathogenic infectious disease: consensus of the European network of infectious disease. Lancet Infect Diseases, 2009, 9(5): 301–311

    Article  Google Scholar 

  43. Cui P, Jin S, Yu L, Wang F, Zhu W, Yang S. Cascading outbreak prediction in networks: a data-driven approach. In Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2013: 901–909

    Chapter  Google Scholar 

  44. Prakash B A, Vrekeen J, Faloutsos C. Spotting culprits in epidemics: how many and which ones? In: Proceedings of the 2012 IEEE 12th International Conference on Data Mining. 2012: 11–20

    Chapter  Google Scholar 

  45. Pasto-Satorras R, Vespignani A. Epidemic spreading in scale-free networks. Physical Review Letters, 2001, 86(4): 3200–3202

    Article  Google Scholar 

  46. Pasto-Satorras R, Vespignani A. Epidemic dynamics and endemic states in complex networks. Physical Review E, 2001, 63(6): 066117

    Article  Google Scholar 

  47. Deijfen M. Epidemics and vaccination on weighted graphs. Mathematical Biosciences, 2011, 232(1): 57–65

    MathSciNet  MATH  Article  Google Scholar 

  48. Britton T, Deijfen M, and Liljeros F. A weighted configuration model and inhomogeneous epidemics. Journal of Statistical Physics, 2011, 145(5): 1368

    MathSciNet  MATH  Article  Google Scholar 

  49. Bollobàs B. Random Graphs. New York: Academic Press, 2001

    MATH  Book  Google Scholar 

  50. Watts D J, Strogatz S H. Collective dynamics of small-world networks. Nature, 1998, 393(6684): 440–442

    Article  Google Scholar 

  51. Barabàsi A L, Albert R. Emergence of scaling in random networks. Science, 1999, 286(543): 509–512

    MathSciNet  Google Scholar 

  52. Pasto-Satorras R, Vespignani A. Epidemic dynamics in finite size scale-free networks. Physical Review E, 2002, 65(3): 035108

    Article  Google Scholar 

  53. Zhou T, Liu J G, Bai W J, Chen G, Wang B H. Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity. Physical Review E, 2006, 74(5): 056109

    Article  Google Scholar 

  54. Liu J, Zhang T. Epidemic spreading of an SEIR model in scale-free networks. Communications in Nonlinear Science and Numerical Simulation, 2011, 16: 3375–3384

    MathSciNet  MATH  Article  Google Scholar 

  55. Zhang H, Fu X. Spreading of epidemics on scale-free networks with nonlinear infectivity. Nonlinear Analysis, 2009, 70(9): 3273–3278

    MathSciNet  MATH  Article  Google Scholar 

  56. Huang C Y, Sun C T, Hsieh J L, Lin H. Simulating SARS: small-world epidemiological modeling and public health policy assessments. Journal of Artificial Societies and Social Simulation, 2004, 7(4). http://jasss.soc.surrey.ac.uk/7/4/2.html

    Google Scholar 

  57. Pastor-Satorras R, Vespignani A. Immunization of complex networks. Physical Review E, 2001, 65(3): 036134

    Google Scholar 

  58. Madar N, Kalisky T, Cohen R, Ben-Avraham D, Havlin S. Immunization and epidemic dynamics in complex networks. European Physical Journal B, 2004, 38(2): 269–276

    Article  Google Scholar 

  59. Li X, Chen G, Li C G. Stability and bifurcation of disease spreading in complex networks. International Journal of Systems Science, 2004, 35(9): 527–536

    MathSciNet  MATH  Article  Google Scholar 

  60. Hayashi Y, Minoura M, Matsukubo J. Oscillatory epidemic prevalence in growing scale-free networks. Physical Review E, 2004, 69(1): 016112

    Article  Google Scholar 

  61. Palla G, Derényi I, Farkas I, Vicsek T. Uncovering the overlapping community structure of complex networks in nature and society. Nature, 2005, 435: 814–818

    Article  Google Scholar 

  62. Chen J, Zhang H, Guan Z H, Li T. Epidemic spreading on networks with overlapping community structure. Physica A, 2012, 391(4): 1848–1854

    Article  Google Scholar 

  63. Griffin R H, Nunn C L. Community structure and the spread of infectious disease in primate social networks. Evolutionary Ecology, 2011, 26(4): 779–800

    Article  Google Scholar 

  64. Cauchemez S, Bhattarai A, Marchbanks T L, Fagan R P, Ostroff S, Ferguson N M, Swerdlow D. Role of social networks in shaping disease transmission during a community outbreak of 2009 H1N1 pandemic influenza. Proceedings of National Academy of Sciences USA, 2011, 108(7): 2825–2830

    Article  Google Scholar 

  65. Wang Y, Zeng D, Cao Z, Wang Y, Song H, Zheng X. The impact of community structure of social contact network on epidemic outbreak and effectiveness of non-pharmaceutical interventions. Lectune Notes in Computer Science, 2011, 6749: 108–120

    Article  Google Scholar 

  66. Barrat A, Barthélemy M, Pastor-Satorras R Vespignani A. The architecture of complex weighted networks. Proceedings of National Academy of Sciences USA, 2004, 101(11): 3747–3752

    Article  Google Scholar 

  67. Bagler G. Analysis of the airport network of India as a complex weighted network. Physica A, 2008, 387(12): 2972–2980

    Article  Google Scholar 

  68. Li M, Fan Y, Chen J, Gao L, Di Z, Wu J. Weighted networks of scientific communication: the measurement and topological role of weight. Physica A, 2005, 350(2–4): 643–656

    Article  Google Scholar 

  69. Onnela J P, Saramäki J, Hyvönen J, Szabo G, Menezes M A D, Kaski K, Barabasi A L, Kertesz J. Analysis of a large-scale weighted network of one-to-one human communication. New Journal of Physics, 2007, 9(6): 179

    Article  Google Scholar 

  70. Zhang B, Horvath S. A general framework for weighted gene coexpression network analysis. Statistical Applications in Genetics and Molecular Biology, 2005, 4: 17

    MathSciNet  Article  Google Scholar 

  71. Li M, Wang J X, Wang H, Pan Y. Identification of essential proteins from weighted protein-protein interaction networks. Journal of Bioinformatics and Computational Biology, 2013, 11(3): 1341002

    MathSciNet  Article  Google Scholar 

  72. Chua H N, Sung W K, Wong L. Exploiting indirect neighbors and topological weight to predict protein function from protein-protein interactions. Bioinformatics, 2006, 22(13): 1623–1630

    Article  Google Scholar 

  73. Dijk D V, Ertaylan G, Boucher C A B, Sloot PMA. Identifying potential survival strategies of HIV-1 through virus-host protein interaction networks. BMC Systems Biology, 2010, 4: 96

    Article  Google Scholar 

  74. Duijn P A C, Kashirin V, Sloot P M A. The relative ineffectiveness of criminal network disruption. Nature Scientific Reports, 2014, 4: 4238

    Google Scholar 

  75. Latora V, Marchiori M. Economic small-world behavior in weighted networks. The European Physical Journal B, 2003, 32(2): 249–263

    Article  Google Scholar 

  76. Harrison F, Sciberras J, James R. Strength of social tie predicts cooperative investment in a human social network. PLoS ONE, 2011, 6(3): e18338

    Article  Google Scholar 

  77. Fagiolo G, Reyes J, Schiavo S. World-trade web: topological properties, dynamics, and evolution. Physical Review E, 2009, 79: 036115

    MathSciNet  Article  Google Scholar 

  78. Yan G, Zhou T, Wang J, Fu Z Q, Wang B H. Epidemic spread in weighted scale-free networks. Chinese Physics Letters. 2005, 22(2): 510–513

    Article  Google Scholar 

  79. Barrat A, Barthélemy M, Vespignani A. Weighted evolving networks: coupling topology and weight dynamics. Physical Review Letters, 2004, 92(22): 228701

    Article  Google Scholar 

  80. Chu X, Guan J, Zhang Z, Zhou S. Epidemic spreading in weighted scale-free networks with community structure. Journal of Statistical Mechanics: Theory and Experiment, 2009, 2009(7): 07043

    Article  Google Scholar 

  81. Chu X, Zhang Z, Guan J, Zhou S. Epidemic spreading with nonlinear infectivity in weighted scale-free networks. Physical A, 2011, 390(3): 471–481

    Article  Google Scholar 

  82. Eames K T D, Read J M, Edmunds W J. Epidemic prediction and control in weighted networks. Epidemics, 2009, 1(1): 70–76

    Article  Google Scholar 

  83. Fournié G, Guitian J, Desvaux S, Cuong V C, Dung D H, Pfeiffer D U, Mangtani P, Ghani A C. Interventions for avian influenza A (H5N1) risk management in live bird market networks. Proceedings of National Academy of Sciences USA, 2013, 110(22): 8751–8752

    Article  Google Scholar 

  84. Duan W, Cao Z, Cui K, Zheng X, Qiu X. Heterogeneous and stochastic agent based models for analyzing infectious diseases’ super spreaders. IEEE Intelligent Systems, 2013, 28(4): 18–25

    Article  Google Scholar 

  85. Yang Z, Zhou T. Epidemic spreading in weighted networks: an edge-based mean-field solution. Physical Review E, 2012, 85(5): 056106

    Article  Google Scholar 

  86. Li R Q, Tang M, Hui P M. Epidemic spreading on multi-relational networks. Acta Physica Sinica, 2013, 62(16): 168903

    Google Scholar 

  87. Kamp C, Moslonka-Lefebvre M, Alizon S. Epidemic spread on weighted networks. PLoS Computational Biology, 2013, 9(12): e1003352

    Article  Google Scholar 

  88. Sun Y, Liu C, Zhang C X, Zhang Z K. Epidemic spreading on weighted complex networks. Physics Letters A, 2014, 378(7–8): 635–640

    MathSciNet  Article  Google Scholar 

  89. Cui A X, Yang Z, Zhou T. Strong ties promote the epidemic prevalence in susceptible-infected-susceptible spreading dynamics. 2013, arXiv:1311.5932v1

    Google Scholar 

  90. Zhu G, Chen G, Xu X J, Fu X. Epidemic spreading on contact networks with adaptive weights. Journal of Theoretical Biology, 2013, 317: 133–139

    MathSciNet  Article  Google Scholar 

  91. Cui A X, Yang Z, Zhou T. Roles of ties in spreading. Cornell University Library, 2012, arXiv: 1204.0100v1

    Google Scholar 

  92. Karsai M, Juhász R, Iglói F. Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks. Physical Review E, 2006, 73: 036116

    Article  Google Scholar 

  93. Yang R, Zhou T, Xie Y B, Lai Y C, Wang B H. Optimal contact process on complex networks. Physical Review E, 2008, 78: 066109

    Article  Google Scholar 

  94. Wu Z X, Peng G, Wang W X, Chan S, Wong E W M. Cascading failure spreading on weighted heterogeneous networks. Journal of Statistical Mechanics: Theory and Experiment, 2008, 2008: P05013

    Google Scholar 

  95. Gross T, D’Lima C J D, Blasius B. Epidemic dynamics on adaptive network. Physical Review Letters, 2006, 96(20): 208701

    Article  Google Scholar 

  96. Gross T, Blasius B. Adaptive coevolutionary networks: a review. Journal of The Royal Society Interface, 2008, 5(20): 259–271

    Article  Google Scholar 

  97. Gross T, Sayama H. Adaptive Networks: Theory, Models and Applications. Berlin: Springer-Verlag, 2009

    Book  Google Scholar 

  98. Shaw L B, Schwartz I B. Fluctuating epidemics on adaptive networks. Physical Review E, 2008, 77(6): 066101

    MathSciNet  Article  Google Scholar 

  99. Shaw L B, Schwartz I B. Enhanced vaccine control of epidemics in adaptive networks. Physical Review E, 2010, 81(4): 046120

    Article  Google Scholar 

  100. Schwartz I B, Shaw L B. Rewiring for adaptation. Physics, 2010, 3(17): 1–6

    Google Scholar 

  101. Lu Y L, Jiang G P, Song Y R. Stability and bifurcation of epidemic spreading on adaptive network. Acta Physica Sinica, 2013, 62(13): 130202

    Google Scholar 

  102. Marceau V, Noël P A, Hébert-Dufresne L, Allard A, Dubé L J. Adaptive networks: coevolution of disease and topology. Physical Review E, 2010, 82(3): 036116

    MathSciNet  Article  Google Scholar 

  103. Yang H, Tang M, Zhang H F. Efficient community-based control strategies in adaptive networks. New Journal of Physics, 2012, 14(12): 123017

    Article  Google Scholar 

  104. Song Y R, Jiang G P, Xu J G. An epidemic spreading model in adaptive networks based on cellular automata. Acta Physica Sinica, 2011, 60(12): 120509

    MATH  Google Scholar 

  105. Jolad S, Liu W, Schmittmann B, Zia R K P. Epidemic spreading on preferred degree adaptive networks. PLoS ONE, 2012, 7(11): e48686

    Article  Google Scholar 

  106. Wang B, Cao L, Suzuki H, Aihara K. Epidemic spread in adaptive networks with multitype agents. Journal of Physics A: Mathematical and Theoretical, 2011, 44(3): 035101

    MathSciNet  Article  Google Scholar 

  107. Demirel G, Gross T. Absence of epidemic thresholds in a growing adaptive network. 2012, arXiv: 1209.2541

    Google Scholar 

  108. Segbroek S V, Santos F C, Pacheco J M. Adaptive contact networks change effective disease infeciousness and dynamics. PLoS Computational Biology, 2010, 6(8): e1000895

    Article  Google Scholar 

  109. Gross T, Kevrekidis I G. Robust oscillations in SIS epidemics on adaptive networks: coarse graining by automated moment closure. Europhysics Letters, 2008, 82(3): 38004

    MathSciNet  Article  Google Scholar 

  110. Zhang H, Small M, Fu X, Sun G, Wang B. Modeling the influence of information on the coevolution of contact networks and the dynamics of infectious diseases. Physics D, 2012, 241(18): 1512–1517

    MATH  Article  Google Scholar 

  111. Risau-Gusman S, Zanette D H. Contact switching as a control strategy for epidemic outbreaks. Journal of Theoretical Biology, 2009, 257(1): 52–60

    MathSciNet  Article  Google Scholar 

  112. Zanette D H, Risau-Gusman S. Infection spreading in a population with evolving contacts. Journal of Biological Physics, 2008, 34(1–2): 135–148

    Article  Google Scholar 

  113. Masuda N, Klemm K, Eguíluz V M. Temporal networks: slowing down diffusion by long lasting interactions. Physical Review Letters, 2013, 111: 188701

    Article  Google Scholar 

  114. Lee S, Rocha L E C, Liljeros F, Holme P. Exploiting temporal network structures of human interaction to effectively immunize populaitons. PLoS ONE, 2012, 7(5): e36439

    Article  Google Scholar 

  115. Holme P. Epidemiologically optimal static networks from temporal network data. PLoS Computational Biology, 2013, 9(7): e1003142

    MathSciNet  Article  Google Scholar 

  116. Dunham J B. An agent-based spatially explicit epidemiological model in MASON. Journal of Artificial Societies and Social Simulation, 2005, 9(1). http://jasss.sos.surrey.ac.uk/9/1/3.html

    Google Scholar 

  117. Jacintho L F O, Batista A F M, Ruas T L, Marietto M G B, Silva F A. An agent-based model for the spread of the Dengue Fever: a swarm platform simulation approach. In: Proceedings of Spring Simulation Multiconference. 2010: 1–8

    Google Scholar 

  118. Roche B, Drake J M, Rohani P. An agent-based model to study the epidemiological and evolutionary dynamics of influenza viruses. BMC Bioinformatics, 2011, 12(87): 1–10

    Google Scholar 

  119. Dion E, Vanschalkwyk L, Lambin E F. The landscape epidemiology of foot-and-mouth disease in South Africa: a spatially explicit multiagent simulation. Ecological Modelling, 2011, 222(13): 2059–2027

    Article  Google Scholar 

  120. Mei S, Sloot P M A, Quax R, Zhu Y, Wang W. Complex agent networks explaining the HIV epidemic among homosexual men in Amsterdam. Mathematics and Computers in Simulation, 2010, 80(5): 1018–1030

    MathSciNet  MATH  Article  Google Scholar 

  121. Yang Y, Atkinson P M, Ettema D. Analysis of CDC social control measures using an agent-based simulation of an influenza epidemic in a city. BMC Infectious Disease, 2011, 11(199): 1–10

    Google Scholar 

  122. Duan W, Cao Z, Ge Y, Qiu X. Modeling and simulation for the spread of H1N1 influenza in school using artificial societies. In: Proceedings of the Pacific Asia Workshop on Intelligence and Security Informatics. 2011: 121–129

    Chapter  Google Scholar 

  123. Liu T, Li X, Liu X P. Integration of small world networks with multiagents systems for simulating epidemic spatiotemporal transmission. Chinese Science Bulletin, 2009, 54(13): 3834–3843

    Article  Google Scholar 

  124. Dibble C, Feidman P G. The GeoGraph 3D computational laboratory network and terrain landscapes for RePast. Journal of Artificial Societies and Social Simulation, 2004, 7(1). http://jasss.soc.surrey.ac.uk/7/1/7.html.

    Google Scholar 

  125. Mniszewski S M, Valle S Y D, Stroud P D, Riese J M, Sydoriak S J. EpiSims simulation of a multicomponent strategy for pandemic in fluenza. In: Proceedings of Spring Simulation Multiconference. 2008: 556–563

    Google Scholar 

  126. Carley K M, Fridsma D B, Casman E, Yahja A, Altman N, Chen L C, Kaminsky B, Nave D. BioWar: scalable agent-based model of bioattacks. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 2006, 36(2): 252–265

    Article  Google Scholar 

  127. Chao D L, Halloran M E, Obenchain V J, Longini I M Jr. FluTE, a publicly available stochastic influenza epidemic simulation model. PLoS Computational Biology, 2010, 6(1): e1000656

    MathSciNet  Article  Google Scholar 

  128. Barrett C, Bisset K, Eubank S G, Feng X, Marathe M V. EpiSimdemics: an efficient and scalable framework for simulating the spread of infectious disease on large social networks. In: Proceedings of the 2008 ACM/IEEE conference on Supercomputing. 2008: 37

    Google Scholar 

  129. Bisset K R, Chen J, Feng X. EpiFast: a fast algorithm for large scale realistic epidemic simulations on distributed memory systems. In: Proceedings of 23rd ACM International Conference on Supercomputing. 2009: 430–439

    Chapter  Google Scholar 

  130. Parker J, Epstein J M. A distributed platform for global-scale agentbased models of disease transmission. ACM Transactions on Modeling and Computer Simulation, 2011, 22(1): 2

    Article  Google Scholar 

  131. Duan W, Cao Z, Wang Y, Zhu B, Daniel Z, Wang F Y, Qiu X, Song H, Wang Y. An ACP approach to public health emergency management: using a campus outbreak of H1N1 influenza as a case study. IEEE Transactions on Systems Man and Cybernetics: Systems, 2013, 43(5): 1028–1041

    Article  Google Scholar 

  132. Wang F Y. Toward a paradigm shift in social computing: the ACP approach. IEEE Intelligent Systems, 2007, 22(5): 65–67

    Article  Google Scholar 

  133. Wang F Y. Parallel control and management for intelligent transportation systems: concepts, architectures, and applications. IEEE Transactions on Intelligent Transportation Systerms, 2010, 11(3): 630–638

    Article  Google Scholar 

  134. Report of the 6th Chinese population census data in 2010. BeiJing Statistical Information Net. http://www.bjstats.gov.cn/xwgb/tjgb/pcgb/201105/t20110504_201363.htm

  135. Guo G, Chen B, Qiu X G, LI Z. Parallel simulation of large-scale artificial society on CPU/GPU mixed architecture. In: Proceedings of the ACM/IEEE/SCS 26th Workshop on Principles of Advanced and Distributed Simulation. 2012: 174–177

    Google Scholar 

  136. Chen B, Guo G. A two-tier parallel architecture for artificial society simulation. In: Proceedings of the ACM/IEEE/SCS 26th Workshop on Principles of Advanced and Distributed Simulation. 2012: 184–186

    Google Scholar 

  137. Edmunds W J, O’Callaghan C J, Nokes D J. Who mixes with whom? A method to determine the contact patterns of adults that may lead to the spread of airborne infections. Proceedings of the Royal Society B, 1997, 264(1384): 949–957

    Article  Google Scholar 

  138. Mossong J, Hens N, Jit M, Beutels P, Auranen K, Mikolajczyk R, Massari M, Salmaso S, Tomba G S, Wallinga J, Heijne J, Malgorzata S T, Rosinska M, Edmunds W J. Social contacts and mixing patterns relevant to the spread of infectious diseases. PLoS Medicine, 2008, 5(3): 381–390

    Article  Google Scholar 

  139. Kretzschmar M, Mikolajczyk R T. Contact profiles in eight European countries and implications for modelling the spread of airborne infectious diseases. PLoS ONE, 2009, 4(6): e5931

    Article  Google Scholar 

  140. Eames K T D, Tilston N L, Ellen B P, Edmunds W J. Measured dynamic social contact patterns explain the spread of H1N1v influenza. PLoS Computational Biology, 2012, 8(3): e1002425

    Article  Google Scholar 

  141. Melegaro A, Jit M, Gay N, Zagheni E, Edmunds W J. What types of contacts are important for the spread of infections? Using contact survey data to explore European mixing patterns. Epidemics. 2011, 3(3–4): 143–151

    Article  Google Scholar 

  142. Ogunjimi B, Hens N, Goeyvaerts N, Aerts M, Damme P V, Beutels P. Using empirical social contact data to model person to person infectious disease transmission: an illustration for varicella. Mathematical Biosciences, 2009, 218(2): 80–87

    MathSciNet  MATH  Article  Google Scholar 

  143. Mikolajczyk R T, Kretzschmar M. Collecting social contact data in the context of disease transmission: prospective and retrospective study designs. Social Networks, 2008, 30(2): 127–135

    Article  Google Scholar 

  144. Edmunds W J, Kafatos G, Wallinga J, Mossong J R. Mixing patterns and the spread of close-contact infectious diseases. Emerging Themes in Epidemiology, 2006, 3(10): 1–8

    Google Scholar 

  145. Wallinga J, Edmunds W J, Kretzschmar M. Perspective: human contact patterns and the spread of airborne infectious diseases. Trends in MicroBiology, 1999, 7(9): 372–377

    Article  Google Scholar 

  146. Beutels P, Shkedy Z, Aerts M, Damme P V. Social mixing patterns for transmission models of close contact infections: exploring self-evaluation and diary-based data collection through a web-based interface. Epidemiology and Infection, 2006, 134(6): 1158–1166

    Article  Google Scholar 

  147. Stehlé J, Voirin N, Barrat A, Cattuto C, Isella L, Pinton J F, Quaggiotto M, Broeck W V D, Régis C, Lina B, Vanhems P. High-resolution measurements of face-to-face contact patterns in a primary school. PLoS ONE, 2011, 6(8): e23176

    Article  Google Scholar 

  148. Wallinga J, Teunis P, Kretzschmar M. Using data on social contacts to estimate age-specific transmission parameters for respiratory-spread infectious agents. American Journal of Epidemiology, 2006, 164(10): 936–944

    Article  Google Scholar 

  149. Salathé M, Kazandjieva M, Lee J W, Levis P, Feldman M W, Jones J H. A high-resolution human contact network for infectious disease transmission. Proceedings of National Academy of Sciences USA, 2010, 107(51): 22020–22025

    Article  Google Scholar 

  150. Isella L, Romano M, Barrat A, Cattuto C, Colizza V, Broeck W V D, Gesualdo F, Pandolfi E, Rava L, Rizzo C, Tozzi A E. Close encounters in a pediatric ward: measuring face-to-face proximity and mixing patterns with wearable sensors. PLoS ONE, 2011, 6(2): e17144

    Article  Google Scholar 

  151. Isella L, Stehlé J, Barrat A, Cattuto C, Pinton J F, Broeck W V D. What’s in a crowd? Analysis of face-to-face behavioral networks. Journal of Theoretical Biology, 2011, 271(1): 166–180

    MathSciNet  Article  Google Scholar 

  152. Zhao K, Stehlé J, Bianconi G, Barrat A. Social network dynamics of face-to-face interactions. Physical Review E, 2011, 83(5): 056109

    Article  Google Scholar 

  153. Moon I C, Carley K M. Modeling and simulating terrorist networks in social and geospatial dimensions. IEEE Intelligent Systems, 2007, 22(5): 40–49

    Article  Google Scholar 

  154. Wang L, Wang Z, Zhang Y, Li X. How human location-specific contact patterns impact spatial transmission between populations? Nature Scientific Reports, 2013, 3: 1468

    Google Scholar 

  155. Barabàsi A L. The origin of bursts and heavy tails in human dynamics. Nature, 2005, 435(7039): 207–211

    Article  Google Scholar 

  156. Oliveira J G, Vazquez A. Impact of interactions on human dynamics. Physica A, 2009, 388(2–3): 187–192

    Article  Google Scholar 

  157. Min B, Goh K I, Vazquez A. Spreading dynamics following bursty human activity patterns. Physical Review E, 2011, 83(3): 036102

    Article  Google Scholar 

  158. Meloni S, Perra N, Arenas A, Gómez S, Moreno Y, Vespignani A. Modeling human mobility responses to the large-scale spreading of infectious diseases. Scientific Reports, 2011, 1(62): 1–7

    Google Scholar 

  159. Merler S, Ajelli M. The role of population heterogeneity and human mobility in the spread of pandemic influenza. Proceedings of the Royal Society B, 2009, 277(1681): 557–567

    Article  Google Scholar 

  160. Zeng D, Chen H, Cao Z, Zhen X. Disease surveillance based on spatial contact networks: a case study of Beijing 2003 SARS epidemic. IEEE Intelligent Systems, 2009, 24(6): 77–82

    Google Scholar 

  161. Keeling M J, Danon L, Vernon M C, House T A. Individual identity and movement networks for disease metapopulations. Proceedings of National Academy of Sciences USA, 2010, 107(19): 8866–8870

    Article  Google Scholar 

  162. Balcan D, Colizza V, Goncalves B, Hu H Ramasco J J, Vespignani A. Multiscale mobility networks and the spatial spreading of infectious diseases. Proceedings of National Academy of Sciences USA, 2009, 106(51): 21484–21489

    Article  Google Scholar 

  163. Codling E A, Plank M J, and Benhamou S. Random walk models in biology. Journal of the Royal Society Interface, 2008, 5(25): 813–834

    Article  Google Scholar 

  164. James A, Plank M J, Edwards A M. Assessing levy walks as models of animal foraging. Journal of the Royal Society Interface, 2011, 8(62): 1233–1247

    Article  Google Scholar 

  165. González MC, Hidalgo C A, Barabási A L. Understanding individual human mobility patterns. Nature, 2008, 453(7196): 779–238

    Article  Google Scholar 

  166. Brockmann D, Hufnagel L, Geisel T. The scaling laws of human travel. Nature, 2006, 439(7075): 462–465

    Article  Google Scholar 

  167. Truscott J, Ferguson N M. Evaluating the adequacy of gravity models as a description of human mobility for epidemic modelling. PLoS Computational Biology, 2012, 8(10): e1002699

    MathSciNet  Article  Google Scholar 

  168. Jandarvo R, Haran M. Bjørnstad O, Grenfell B. Emulating a gravity model to infer the spatialtemporal dynamics of an infectious disease. http://arxiv.org/pdf/1110.6451v3.pdf

  169. Li X, Tian H, Lai D, Zhang Z. Validation of the gravity model in predicting the global spread of influenza. International Journal of Environmental Research and Public Health, 2011, 8(8): 3134–3143

    Article  Google Scholar 

  170. Meloni S, Arenas A, and Moreno Y. Traffic-driven epidemic spreading in finite-size scale-free network. Proceedings of National Academy of Sciences USA, 2009, 106(40): 16897–16902

    Article  Google Scholar 

  171. Epstein J M, Goedecke D M, Yu F, Morris R J, Wagener D K, Bobashev G V. Controlling pandemic flu: the value of international air travel restrictions. PLoS ONE, 2007, 2(5): e401

    Article  Google Scholar 

  172. Duan W, Qiu X. Fostering artificial societies using social learning and social control in parallel emergency management systems. Frontiers of Computer Science, 2012, 6(5), 604–610

    MathSciNet  Google Scholar 

  173. Zheng X, Zhong Y, Zeng D, Wang F Y. Social influence and spread dynamics in social networks. Frontiers of Computer Science, 2012, 6(5), 611–620

    MathSciNet  Google Scholar 

  174. Hufnagel L, Brockmann D, Geisel T. Forecast and control epidemics in a globalized world. Proceedings of National Academy of Sciences USA, 2004, 101(42): 15124–15129

    Article  Google Scholar 

  175. Watts D J, Muhamad R, Medina D C, Dodds P S. Multiscale, resurgent epidemics in a hierarchical metapopulation model. Proceedings of National Academy of Sciences USA, 2005, 102(32): 11157–11162

    Article  Google Scholar 

  176. Colizza V, Barrat A, Barthélemy M, Vespignani A. Epidemic predictability in meta-population models with heterogeneous couplings: the impact of disease parameter values. International Journal of Bifurcation and Chaos, 2007, 17(7): 2491–2500

    MathSciNet  MATH  Article  Google Scholar 

  177. Colizza V, Barrat A, Barthélemy M, Valleron A J, Vespignani A. Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions. PLoS Medicine, 2007, 4(1): e13

    Article  Google Scholar 

  178. Savini L, Weiss C, Colangeli P, Conte A, Ippoliti C, Lelli R, Santucci U. A web-based geographic information system for the management of animal disease epidemics. Veterinaria Italiana, 2007, 43(3): 761–772

    Google Scholar 

  179. Laosuwan T. Online web GIS-based services for spatial data and sharing of leptospirosis epidemiology information; development of pilot project in Mahasarakham province Thailand. International Journal of Geomatics and Geosciences, 2012, 3(1): 121–133

    Google Scholar 

  180. Woolhouse M E J, Dye C, Etard J F, Smith T, Charlwood J D, Garnett G P, Hagan P, Hii J L K, Ndhlovu P D, Quinnell R J, Watts C H, Chandiwana S K, Anderson R M. Heterogeneities in the transmission of infectious agents: implications for the design of control programs. Proceedings of National Academy of Sciences USA, 1997, 94(1): 338–342

    Article  Google Scholar 

  181. Xuan H, Xu L, Li L. A CA-based epidemic model for HIV/AIDS transmission with heterogeneity. Annals Operations Research, 2009, 168(1): 81–99

    MathSciNet  MATH  Article  Google Scholar 

  182. Lafuerza L F, Toral R. On the effect of heterogeneity in stochastic interacting-particle systems. Scientific Reports, 2013, 3: 1189

    Article  Google Scholar 

  183. Galvani A P, May R M. Dimensions of super spreading. Nature, 2005, 438(7066): 293–295

    Article  Google Scholar 

  184. Lloyd-Smith J O, Schreiber S J, Kopp P E, Getz W M. Super spreading and the effect of individual variation on disease emergency. Nature, 2005, 438(7066): 355–359

    Article  Google Scholar 

  185. Stein R A. Super-spreaders in infectious diseases. International Journal of Infectious Diseases, 2011, 15(8): e510–e513

    Article  Google Scholar 

  186. Small M, Tse C K, Walker D M. Super-spreader and the rate of transmission of the SARS virus. Physica D, 2006, 215(2): 146–158

    MathSciNet  MATH  Article  Google Scholar 

  187. Yang R, Wang B H, Ren J, Bai W J, Shi Z W, Wang W X, Zhou T. Epidemic spreading on heterogeneous networks with identical infectivity. Physics Letters A, 2007, 364(3–4): 189–193

    MATH  Article  Google Scholar 

  188. Wang J Z, Liu Z R, Xu J. Epidemic spreading on uncorrelated heterogeneous networks with non-uniform transmission. Physica A, 2007, 382(2): 715–721

    Article  Google Scholar 

  189. Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A. Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. Journal of Theoretical Biology, 2005, 235(2): 275–288

    MathSciNet  Article  Google Scholar 

  190. Ferguson N. Capturing human behaviour. Nature. 2007, 446: 733

    Article  Google Scholar 

  191. Funk S, Salathé M Jansen V A. Modeling the influence of human behaviour on the spread of infectious disease: a review. Journal of the Royal Society Interface, 2010, 7(50): 1247–1256

    Article  Google Scholar 

  192. Auld M C. Choices, beliefs, and infectious disease dynamics. Journal of Health Economics. 2003, 22(3): 361–377

    Article  Google Scholar 

  193. Zhang H, Zhang J, Li P, Small M, Wang B. Risk estimation of infectious diseases determines the effectiveness of the control strategy. Physica D, 2011, 240(11): 943–948

    MATH  Article  Google Scholar 

  194. Chen F H. Modeling the effect of information quality on risk behavior change and the transmission of infectious disease. Mathematical Biosciences, 2009, 217(2): 125–133

    MathSciNet  MATH  Article  Google Scholar 

  195. Shim E, Chapman G B, Galvani A P. Decision making with regard to antiviral intervention during an influenza pandemic. Medicine Decision Making, 2010, 30(4): e64–e81

    Google Scholar 

  196. Fu F, Rosenbloom D I, Wang L, Nowak M A. Imitation dynamics of vaccination behaviour on social network. Proceedings of the Royal Society B, 2011, 278(1702): 42–49

    Article  Google Scholar 

  197. Reluga T C. Game theory of social distancing in response to an epidemic. PLoS Computational Biology, 2010, 6(5): e1000793

    MathSciNet  Article  Google Scholar 

  198. Bauch C T, Galvani A P, Earn D J D. Group interest versus self-interest in smallpox vaccination policy. Proceedings of National Academy of Sciences USA, 2003, 100(18): 10564–10567

    MathSciNet  MATH  Article  Google Scholar 

  199. Rosenstock I M. The health belief model and preventive health behavior. Health Education & Behavior, 1974, 2(4): 354–386

    Article  Google Scholar 

  200. Ajzen I, Fishbein M. Understanding Attitudes and Predicting Social Behavior. Englewood Cliffs: Prentice-Hall, 1980: 1–278

    Google Scholar 

  201. Bandura A. Self-efficacy: the Exercise of Control. New York: Freeman, 1997: 1–600.

    Google Scholar 

  202. Rogers R W. A Cognitive and Physiological Process in Fear Appeals and Attitude Change: a Revised Theory of Protection Motivation. New York: Guilford, 1983: 153–176

    Google Scholar 

  203. Hayden J A. Introduction to Health Behavior Theory. Jones and Bartlett, 2009: 1–148

    Google Scholar 

  204. Durham D P, Casman E A. Incorporating individual health-protective decisions into disease transmission models: a mathematical framework. Journal of the Royal Society Interface, 2012, 9(68): 562–570

    Article  Google Scholar 

  205. Durham D P, Casman E A, Albert S M. Deriving behavior model parameters from survey data: self-protective behavior adoption during the 2009–2010 influenza A (H1N1) pandemic. Risk Analysis, 2012, 32(12): 2020–2031

    Article  Google Scholar 

  206. Tang C S, Wong C. Factors influencing the wearing of facemasks to prevent the severe acute respiratory syndrome among adult Chinese in Hong Kong. Preventive Medicine, 2004, 39(6): 1187–1193

    Article  Google Scholar 

  207. D’Onofrio A, Manfredi P. Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases. Journal of Theoretical Biology, 2008, 256(3): 473–478

    MathSciNet  Article  Google Scholar 

  208. Zhang H F, Zhang W Y, Sun G Q, Zhou T, Wang B H. Time-delayed information can induce the periodic outbreaks of infectious diseases (in Chinese). Scientia Sinnica Physica, Mechanica & Astronomica, 2012, 42(6): 631–638

    Article  Google Scholar 

  209. Kiss I Z, Cassell J, Recker M, Simon P L. The impact of information transmission on epidemic outbreaks. Mathematical Biosciences, 2010, 225(1): 1–10

    MathSciNet  MATH  Article  Google Scholar 

  210. Gong X, Xiao R. Research on multi-agent simulation of epidemic news spread characteristics. Journal of Artificial Societies and Social Simulation, 2007, 10(31). http://jasss.soc.surrey.ac.uk/10/3/1.html

    Google Scholar 

  211. Myers S, Zhu C, Leskovec J. Information diffusion and external influence in networks. In: Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining. 2012: 33–41

    Chapter  Google Scholar 

  212. Cui P, Wang F, Liu S, Ou M, Yang S, Sun L. Who should share what? Item-level social influence prediction for users and posts ranking. In: Proceedings of the 34th international ACM SIGIR conference on Research and development in Information Retrieval. 2011: 185–194

    Google Scholar 

  213. Mao L, Bian L. Agent-based simulation for a dual diffusion process of influenza and human preventive behavior. International Journal of Geographical Information Science, 2011, 25(9): 1371–1388

    Article  Google Scholar 

  214. Funk S, Gilad E, Watkins C, Jansen V A. The spread of awareness and its impact on epidemic outbreaks. Proceedings of National Academy of Sciences USA, 2009, 106(16): 6872–6877

    MATH  Article  Google Scholar 

  215. Tommasi M, Weinschelbaum F. Centralization vs. decentralization: a principal-agent analysis. Journal of Public Economic Theory, 2007, 9(2): 369–389

    Article  Google Scholar 

  216. Dredze M. How social media will change public health. IEEE Intelligent Systems, 2012, 27(4): 81–84

    Article  Google Scholar 

  217. Rahmandad D, Sterman J. Heterogeneous and network structure in the dynamics of diffusion: comparing agent-based and differential equation models. Management Science, 2008, 54(5): 998–1014

    Article  Google Scholar 

  218. Bagni R, Berchi R, Cariello P. A comparison of simulation models applied to epidemics. Journal of Artificial Societies and Social Simulation, 2002, 5(3). http://jasss.soc.surrey.ac.uk/53/5.html

    Google Scholar 

Download references

Author information

Affiliations

  1. Center of Computational Experiments and Parallel Systems Technology, College of Information Systems and Management, National University of Defense Technology, Changsha, 410073, China

    Wei Duan, Zongchen Fan, Peng Zhang, Gang Guo & Xiaogang Qiu

Authors
  1. Wei Duan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zongchen Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gang Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiaogang Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Duan.

Additional information

Wei Duan received PhD degree in 2014 in control science and engineering from the National University of Defense Technology, China. His research interests include complex networks, epidemic modeling, information diffusion, agent-based simulation, and social computing.

Zongchen Fan is a PhD candidate in the College of Information Systems and Management, National University of Defense Technology, China. His research interests include agent-based modeling and simulation, opinion dynamics, and parallel emergency management.

Peng Zhang received his BS degree in 2009 and his MS degree in 2011 in control science and engineering from the National University of Defense Technology, China, where he is currently a PhD candidate. His research interests include artificial societies, domain specific modeling and knowledge engineering.

Gang Guo received his BS degree in 1999 and his PhD degree in 2004 in control science and engineering from the National University of Defense Technology, China. His research interests include environment modeling and simulation, and simulation software and platforms.

Xiaogang Qiu received his PhD degree in system simulation from the National University of Defense Technology, China. He is a professor in the College of Information Systems and Management, National University of Defense Technology, China. His research interests include simulation, multi-agent systems, knowledge management, and parallel control.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Duan, W., Fan, Z., Zhang, P. et al. Mathematical and computational approaches to epidemic modeling: a comprehensive review. Front. Comput. Sci. 9, 806–826 (2015). https://doi.org/10.1007/s11704-014-3369-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11704-014-3369-2

Keywords

  • mathematics
  • complex networks
  • agent-based models
  • epidemicmodeling
  • human dynamics
  • infectious diseases