Congruent epidemic models for unstructured and structured populations: Analytical reconstruction of a 2003 SARS outbreak

Mathematical Biosciences

Volumn 203, Issue 2, 2006, Pages 171-203

  Bombardt, John N ^a  

^a INSTITUTE FOR DEFENSE ANALYSES   (United States)

Author keywords

Deterministic epidemic model; Preferred mixing; SARS; Scale free network; Time dependent transmission rate

Indexed keywords

DETERMINISTIC EPIDEMIC MODELS; PREFERRED MIXING; SARS; SCALE-FREE NETWORKS; TIME-DEPENDENT TRANSMISSION RATE;

COMPUTER SIMULATION; DISEASE CONTROL; MONTE CARLO METHODS; POPULATION STATISTICS; PROBABILITY DENSITY FUNCTION;

EPIDEMIOLOGY;

SEVERE ACUTE RESPIRATORY SYNDROME VACCINE;

DISEASE SPREAD; DISEASE TRANSMISSION; EPIDEMIC; EPIDEMIOLOGY; INFECTIOUS DISEASE; MONTE CARLO ANALYSIS; POPULATION DENSITY; POPULATION DYNAMICS;

ANALYTIC METHOD; ARTICLE; DENSITY FUNCTIONAL THEORY; DISEASE CONTROL; DISEASE COURSE; DISEASE TRANSMISSION; EPIDEMIC; INFECTION RATE; MONTE CARLO METHOD; POPULATION DYNAMICS; POPULATION MODEL; POPULATION STRUCTURE; PROBABILITY; SEVERE ACUTE RESPIRATORY SYNDROME; TAIWAN; VACCINATION;

DISEASE OUTBREAKS; DISEASE TRANSMISSION, HORIZONTAL; DISEASE TRANSMISSION, INFECTIOUS; HUMANS; MODELS, BIOLOGICAL; POPULATION DYNAMICS; SARS VIRUS; SEVERE ACUTE RESPIRATORY SYNDROME; TAIWAN;

EID: 33749055091     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2006.05.004     Document Type: Article

References (48)

1. United States General Accounting Office, Emerging Infectious Diseases: Asian SARS Outbreak Challenged International and National Responses, GAO-04-564, April 2004, p. 3.
2. Lloyd-Smith J.O., Galvani A.P., and Getz W.M. Curtailing transmission of severe acute respiratory syndrome within a community and its hospital. Proc. R. Soc. Lond. B 270 (2003) 1979
3. 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., Lo S.-V., Leung P.-Y., Tsang T., Ho W., Lee K.-H., Lau E.M.C., Ferguson N.M., and Anderson R.M. Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science 300 (2003) 1961
4. 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., and Murray M. Transmission dynamics and control of severe acute respiratory syndrome. Science 300 (2003) 1966
5. Fraser C., Riley S., Anderson R.M., and Ferguson N.M. Factors that make an infectious disease outbreak controllable. PNAS 101 (2004) 6146
6. Hethcote H.W., and Van Ark J.W. Epidemiological models for heterogeneous populations: proportionate mixing, parameter estimation, and immunization programs. Math. Biosci. 84 (1987) 85
7. Albert R., and Barabasi A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74 (2002) 47
8. Dorogovtsev S.N., and Mendes J.F.F. Evolution of random networks. Adv. Phys. 51 (2002) 1079
9. Krapivsky P.L., and Redner S. Organization of growing random networks. Phys. Rev. E 63 (2001) 066123
10. May R.M., and Lloyd A.L. Infection dynamics on scale-free networks. Phys. Rev. E 64 (2001) 066112
11. Pastor-Satorras R., and Vespignani A. Epidemic spreading in scale-free networks. Phys. Rev. Lett. 86 (2001) 3200
12. Moreno Y., Pastor-Satorras R., and Vespignani A. Epidemic outbreaks in complex heterogeneous networks. Eur. Phys. J. B 26 (2002) 521
13. Pastor-Satorras R., and Vespignani A. Epidemic dynamics in finite size scale-free networks. Phys. Rev. E 65 (2002) 035108
14. Boguna M., Pastor-Satorras R., and Vespignani A. Absence of epidemic threshold in scale-free networks with degree correlations. Phys. Rev. Lett. 90 (2003) 029701
15. Barthelemy M., Barrat A., Pastor-Satorras R., and Vespignani A. Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. Phys. Rev. Lett. 92 (2004) 178701
16. Barthelemy M., Barrat A., Pastor-Satorras R., and Vespignani A. Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. J. Theo. Biol. 235 (2005) 275
17. Masuda N., Konno N., and Aihara K. Transmission of severe acute respiratory syndrome in dynamical small-world networks. Phys. Rev. E 69 (2004) 031917
18. Small M., and Tse C.K. Clustering model for transmission of the SARS virus: application to epidemic control and risk assessment. Physica A 351 (2005) 499
19. Schneeberger A., Mercer C.H., Gregson S.A.J., Ferguson N.M., Nyamukapa C.A., Anderson R.M., Johnson A.M., and Garnett G.P. Scale-free networks and sexually transmitted diseases: a description of observed patterns of sexual contacts in Britain and Zimbabwe. Sexually Transmitted Diseases 31 (2004) 380
20. Keeling M.J., and Grenfell B.T. Disease extinction and community size: modeling the persistence of measles. Science 275 (1997) 65
21. Lloyd A.L. Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods. Proc. R. Soc. Lond. B 268 (2001) 985
22. Krapivsky P.L., and Redner S. Finiteness and fluctuations in growing networks. J. Phys. A: Math. Gen. 35 (2002) 9517
23. Newman M.E.J. The structure and function of complex networks. SIAM Rev. 45 (2003) 167
24. Hsieh Y.-H., Chen C.W.S., and Hsu S.-B. SARS outbreak, Taiwan, 2003. Emerg. Infect. Dis. 10 2 (2004) 201. Available from:
25. Hsu S.-B., and Hsieh Y.-H. Modeling intervention measures and severity-dependent public response during severe acute respiratory syndrome outbreak. SIAM J. Appl. Math. 66 2 (2006) 627
26. Zhou Y., Ma Z., and Brauer F. A discrete epidemic model for SARS transmission and control in China. Mathematical and Computer Modelling 40 (2004) 1491
27. Zhang J., Lou J., Ma Z., and Wu J. A compartmental model for the analysis of SARS transmission patterns and outbreak control measures in China. Appl. Math. Comput. 162 (2005) 909
28. Gumel A.B., Ruan S., Day T., Watmough J., Brauer F., van den Driessche P., Gabrielson D., Bowman C., Alexander M.E., Ardal S., Wu J., and Sahai B.M. Modelling strategies for controlling SARS outbreaks. Proc. R. Soc. Lond. B 271 (2004) 2223
29. Morbidity and Mortality Weekly Report, Use of Quarantine to Prevent Transmission of Severe Acute Respiratory Syndrome: Taiwan, 2003, Vol. 52 (No. 29), July 25, 2003, p. 680.
30. Center for Disease Control, Department of Health, Executive Yuan, Taiwan, Memoir of Severe Acute Respiratory Syndrome Control in Taiwan, October 2003.
31. R.M. Anderson, C. Fraser, A.C. Ghani, C.A. Donnelly, S. Riley, N.M. Ferguson, G.M. Leung, T.H. Lam, A.J. Hedley, Epidemiology, transmission dynamics and control of SARS: the 2002-2003 epidemic, Phil. Trans. R. Soc. Lond. B 04tb010g.2 (2004).
32. Cheng P.K.C., Wong D.A., Tong L.K.L., Ip S.-M., Lo A.C.T., Lau C.-S., Yeung E.Y.H., and Lim W.W.L. Viral shedding patterns of coronavirus in patients with probable severe acute respiratory syndrome. Lancet 363 (2004) 1699
33. Hsieh Y.-H., King C.-C., Chen C.W.S., Ho M.-S., Lee J.-Y., Liu F.-C., Wu Y.-C., and Wu J.-S.J. Quarantine for SARS, Taiwan. Emerging Infectious Diseases 11 2 (2005) 278. Available from:
34. Chowell G., Castillo-Chavez C., Fenimore P.W., Kribs-Zaleta C.M., Arriola L., and Hyman J.M. Model parameters and outbreak control for SARS. Emerg. Infect. Dis. 10 7 (2004) 1258. www.cdc.gov/eid
35. Donnelly C.A., Ghani A.C., Leung G.M., Hedley A.J., Fraser C., Riley S., Abu-Raddad L.J., Ho L.-M., Thach T.-Q., Chau P., Chan K.-P., Lam T.-H., Tse L.-Y., Tsang T., Liu S.-H., Kong J.H.B., Lau E.M.C., Ferguson N.M., and Anderson R.M. Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong. Lancet 361 (2003) 1761
36. Hong Kong Health, Welfare & Food Bureau, SARS Bulletin, May 28, 2003.
37. May R.M., and Anderson R.M. The transmission dynamics of human immunodeficiency virus (HIV). Phil. Trans. R. Soc. Lond. B 321 (1988) 565
38. J.N. Bombardt, H.E. Brown, Potential Influenza Effects on Military Populations, Institute for Defense Analyses Paper P-3786, December 2003.
39. Krapivsky P.L., Redner S., and Leyvraz F. Connectivity of growing random networks. Phys. Rev. Lett. 85 (2000) 4629
40. Krapivsky P.L., and Redner S. Finiteness and fluctuations in growing networks. J. Phys. A: Math. Gen. 35 (2002) 9517
41. Barabasi A.-L., and Albert R. Emergence of scaling in random networks. Science 286 (1999) 509
42. Hethcote H.W. Modeling heterogeneous mixing in infectious disease dynamics. In: Isham V., and Medley G. (Eds). MODELS FOR INFECTIOUS HUMAN DISEASES: Their Structure and Relation to Data (1996), Cambridge University 215
43. Boguna M., and Pastor-Satorras R. Epidemic spreading in correlated complex networks. Phys. Rev. E 66 (2002) 047104
44. Pastor-Satorras R., Vazquez A., and Vespignani A. Dynamical and correlation properties of the internet. Phys. Rev. Lett. 87 (2001) 258701
45. Ramasco J.J., Dorogovtsev S.N., and Pastor-Satorras R. Self-organization of collaboration networks. Phys. Rev. E 70 (2004) 036106
46. Newman M.E.J. Assortative mixing in networks. Phys. Rev. Lett. 89 (2002) 208701
47. Wallinga J., and Teunis P. Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures. Am J. Epidemiol. 160 (2004) 509
48. Meyers L.A., Pourbohloul B., Newman M.E.J., Skowronski D.M., and Brunham R.C. Network theory and SARS: predicting outbreak diversity. J. Theo. Biol. 232 1 (2005)