Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models

References

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