Heterogeneity and network structure in the dynamics of diffusion: Comparing agent-based and differential equation models

Management Science

Volumn 54, Issue 5, 2008, Pages 998-1014

  Rahmandad, Hazhir ^a   Sterman, John ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Agent based models; Complex adaptive systems; Epidemiology; Heterogeneity; Networks; Scale free; SEIR model; Simulation; Small world; System dynamics

Indexed keywords

AGENT-BASED MODELS; COMPLEX ADAPTIVE SYSTEMS; HETEROGENEITY; NETWORKS; SCALE FREE; SEIR MODEL; SIMULATION; SMALL WORLD; SYSTEM DYNAMICS;

ADAPTIVE SYSTEMS; COST BENEFIT ANALYSIS; DIFFUSION; DISEASES; DYNAMICS; ELECTRIC NETWORK TOPOLOGY; RANDOM PROCESSES; SENSITIVITY ANALYSIS;

STOCHASTIC MODELS;

EID: 61849110802     PISSN: 00251909     EISSN: 15265501     Source Type: Journal    
DOI: 10.1287/mnsc.1070.0787     Document Type: Article

References (68)

1. Abbey, H. 1952. An examination of the reed-frost theory of epidemics. Human Biol. 24(3) 201-233.
2. Ahuja, M., K. Carley. 1999. Network structure in virtual organizations. Organ. Sci. 10(6) 741-757.
3. Anderson, R. M., R. M. May. 1991. Infectious Diseases of Humans Dynamics and Control. Oxford University Press, Oxford, UK.
4. Axelrod, R. 1997. The dissemination of culture-A model with local convergence and global polarization. J. Conflict Resolution 41(2) 203-226.
5. Axtell, R., J. Axelrod, J. M. Epstein, M. Cohen. 1996. Aligning simulation models: A case study and results. Computational Math. Organ. Theory 1(2) 123-141.
6. Axtell, R., J. Epstein, J. S. Dean, G. J. Gumerman, A. C. Swedlund, J. Harburger, S. Chakravarty, R. Hammond, J. Parker, M. Parker. 2002. Population growth and collapse in a multiagent model of the Kayenta Anasazi in Long House Valley. Proc. Natl. Acad. Sci. USA 99(Suppl. 3) 7275-7279.
7. Ball, F., D. Mollison, G. Scalia-Tomba. 1997. Epidemics with two levels of mixing. Ann. Appl. Probab. 7(1) 46-89.
8. Barabasi, A. L. 2002. Linked: How Everything Is Connected to Everything Else and What It Means. Perseus, Cambridge, MA.
9. Barabasi, A. L., R. Albert. 1999. Emergence of scaling in random networks. Science 286(5439) 509-512.
10. Bass, F. 1969. A new product growth model for consumer durables. Management Sci. 15(5) 215-227.
11. Bjornstad, O., M. Peltonen, A. M. Liebhold, W. Baltensweiler. 2002. Waves of larch budmoth outbreaks in the European Alps. Science 298(5595) 1020-1023.
12. Blower, S. M., H. B. Gershengorn, R. M. Grant. 2000. A tale of two futures: HIV and antiretroviral therapy in San Francisco. Science 287(5453) 650-654.
13. Carley, K. 1992. Organizational learning and personnel turnover. Organ. Sci. 3(1) 20-46.
14. Chen, L. C., B. Kaminsky, T. Tummino, K. M. Careley, E. Casman, D. Fridsma, A. Yahja. 2004. Aligning simulation models of smallpox outbreaks. Proc. 2nd Sympos. on Intelligence and Security Informatics, Tucson, AZ, 1-16.
15. Davis, G. 1991. Agents without principles? The spread of the poison pill through the intercorporate network. Admin. Sci. Quart. 36 583-613.
16. Dye, C., N. Gay. 2003. Modeling the SARS epidemic. Science 300(5627) 1884-1885.
17. Edwards, M., S. Huet, F. Goreaud, G. Deffuant. 2003. Comparing an individual-based model of behavior diffusion with its mean field aggregate approximation. J. Artificial Societies Soc. Simulation 6(4). http://jasss.soc.surrey.ac.uk/6/4/9.html.
18. Epstein, J. M. 2006. Generative Social Science: Studies in Agent-Based Computational Modeling. Princeton University Press, Princeton, NJ.
19. Epstein, J. M., D. Cummings, S. Chakravarty, R. M. Singa, D. S. Burke. 2004. Toward a Containment Strategy for Smallpox Bioterror-An Individual-Based Computational Approach. Brookings Institution Press, Washington, D.C.
20. Erdos, P., A. Renyi. 1960. On the evolution of random graphs. Publ. Math. Inst. Hungarian Acad. Sci. 5 17-61.
21. Eubank, S., H. Guclu, V. S. A. Kumar, M. V. Marathe, A. Srinivasan, Z. Toroczkai, N. Wang. 2004. Modelling disease outbreaks in realistic urban social networks. Nature 429(6988) 180-184.
22. Fahse, L., C. Wissel, V. Grimm. 1998. Reconciling classical and individual-based approaches in theoretical population ecology: A protocol for extracting population parameters from individual-based models. Amer. Naturalist 152(6) 838-852.
23. Ferguson, N. M., M. J. Keeling, J. W. Edmunds, R. Gani, B. T. Grenfell, R. M. Anderson, S. Leach. 2003. Planning for smallpox outbreaks. Nature 425(6959) 681-685.
24. Gani, J., S. Yakowitz. 1995. Error bounds for deterministic approximations to Markov processes, with applications to epidemic models. J. Appl. Probab. 32(4) 1063-1076.
25. Gani, R., S. Leach. 2001. Transmission potential of smallpox in contemporary populations. Nature 414(6865) 748-751.
26. Gibbons, D. E. 2004. Network structure and innovation: Ambiguity effects on diffusion in dynamic organizational fields. Acad. Management J. 47(6) 938-951.
27. Glass, T., M. Schoch-Spana. 2002. Bioterrorism and the people: How to vaccinate a city against panic. Clinical Infectious Diseases 34(2) 217-223.
28. Greenhalgh, D., F. Lewis. 2001. Stochastic models for the spread of HIV amongst intravenous drug users. Stochastic Models 17(4) 491-512.
29. Halloran, E., I. Longini, N. Azhar, Y. Yang. 2002. Containing bioterrorist smallpox. Science 298(5597) 1428-1432.
30. Hethcote, H. W. 2000. The mathematics of infectious diseases. SIAM Rev. 42(4) 599-653.
31. Jacquez, J. A., P. O'Neill. 1991. Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations. Math. Biosciences 107(2) 161-186.
32. Jacquez, J. A., C. P. Simon. 1993. The stochastic SI model with recruitment and deaths.1. Comparison with the closed SIS model. Math. Biosciences 117(1-2) 77-125.
33. Jacquez, J. A., C. P. Simon. 2002. Qualitative theory of compartmental systems with lags. Math. Biosciences 180 329-362.
34. Kaplan, E. H., L. M. Wein. 2003. Smallpox bioterror response. Science 300(5625) 1503.
35. Kaplan, E. H., D. Craft, L. Wein. 2002. Emergency response to a smallpox attack: The case for mass vaccination. Proc. Natl. Acad. Sci. USA 99(16) 10935-10940.
36. Kaplan, E. H., D. Craft, L. Wein. 2003. Analyzing bioterror response logistics: The case of smallpox. Math. Biosciences 185(1) 33-72.
37. Kasperson, R., O. Renn, P. Slovic, H. S. Brown, J. Emel, R. Globle, J. X. Kasperson, S. Ratick. 1988. The social amplification of risk: A conceptual framework. Risk Anal. 8(2) 177-187.
38. Keeling, M. 1999. The effects of local spatial structure on epidemiological invasions. Proc. Roy. Soc. London Series B-Biological Sci. 266(1421) 859-867.
39. Koopman, J. S. 2002. Controlling smallpox. Science 298(5597) 1342-1344.
40. Koopman, J. S., G. Jacquez, S. E. Chick. 2001. New data and tools for integrating discrete and continuous population modeling strategies. Ann. New York Acad. Sci. 954(1) 268-294.
41. Koopman, J. S., S. E. Chick, C. P. Simon, C. S. Riolo, G. Jacquez. 2002. Stochastic effects on endemic infection levels of disseminating versus local contacts. Math. Biosciences 180(1-2) 49-71.
42. Kossinets, G., D. Watts. 2006. Empirical analysis of an evolving social network. Science 311(5757) 88-90.
43. Levinthal, D., J. G. March. 1981. A model of adaptive organizational search. J. Econom. Behav. Organ. 2(4) 307-333.
44. Lightfoot, M., D. Swendeman, M. J. Rotheram-Borus, W. S. Comulada, R. Weiss. 2005. Risk behaviors of youth living with HIV pre- and post-HAART. Amer. J. Health Behav. 29(2) 162-171.
45. Lipsitch, M., T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, G. Gopalakrishna, S. K. Chew, C. C. Tan, M. H. Samore, D. Fisman, M. Murray. 2003. Transmission dynamics and control of severe acute respiratory syndrome. Science 300(5627) 1966-1970.
46. Lomi, A., E. R. Larsen. 2001. Dynamics of Organizations Computational Modeling and Organization Theories. AAAI Press/MIT Press, Menlo Park, CA.
47. Mahajan, V., E. Muller, Y. Wind. 2000. New-Product Diffusion Models. Kluwer Academic Publishers, Boston.
48. May, R. M. 2004. Uses and abuses of mathematics in biology. Science 303(5659) 790-793.
49. McCloskey, D., S. Ziliak. 1996. The standard error of regressions. J. Econom. Literature 34(1) 97-114.
50. Meadows, D. H., J. Robinson. 1985. The Electronic Oracle Computer Models and Social Decisions. John Wiley & Sons, Chichester, UK.
51. Murray, J. D. 2002. Mathematical Biology. Springer, New York.
52. Newman, M. 2002. Spread of epidemic disease on networks. Physical Rev. E 66(1) 016128-1-016128-11.
53. Newman, M. 2003. The structure and function of complex networks. SIAM Rev. 45(2) 167-256.
54. Reynolds, C. 1987. Flocks, herds, and schools: A distributed behavioral model. Comput. Graphics 21(4) 25-34.
55. Riley, S. 2007. Large-scale spatial-transmission models of infectious disease. Science 316(5627) 1298-1301.
56. Riley, S., C. Fraser, C. A. Donnelly, A. C. Ghani, L. J. Abu-Raddad, A. J. Hedley, G. M. Leung, L. M. Ho, T. H. Lam, T. Q. Thach, P. Chau, K. P. Chan, P. Y. Leung, T. Tsang, W. Ho, K. H. Lee, E. M. C. Lau, N. M. Ferguson, R. M. Anderson. 2003. Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions. Science 300(5627) 1961-1966.
57. Rogers, E. 2003. Diffusion of Innovations. Free Press, New York.
58. Schelling, T. 1978. Micromotives and Macrobehavior. Norton, New York.
59. Shnerb, N., Y. Louzoun, E. Bettelheim, S. Solomon. 2000. The importance of being discrete: Life always wins on the surface. Proc. Natl. Acad. Sci. USA 97(19) 10322-10324.
60. Sterman, J. 2000. Business Dynamics Systems Thinking and Modeling for a Complex World. Irwin/McGraw-Hill, New York.
61. Strang, D., S. Soule. 1998. Diffusion in organizations and social movements from hybrid corn to poison pills. Annual Rev. Sociol. 24 265-290.
62. Tesfatsion, L. 2002. Economic agents and markets as emergent phenomena. Proc. Natl. Acad. Sci. USA 99(Suppl. 3) 7191-7192.
63. Urban, G., J. Hauser, J. Roberts. 1990. Prelaunch forecasting of new automobiles. Management Sci. 36(4) 401-421.
64. Veliov, V. 2005. On the effect of population heterogeneity on dynamics of epidemic diseases. J. Math. Biol. 51(2) 123-143.
65. Wallinga, J., P. Teunis. 2004. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Amer. J. Epidemiology 160(6) 509-516.
66. Watts, D. 1999. Small Worlds. Princeton University Press, Princeton, NJ.
67. Watts, D. 2004. The new science of networks. Annual Rev. Sociol. 30 243-270.
68. Watts, D., S. Strogatz. 1998. Collective dynamics of small-world networks. Nature 393(6684) 440-442.