Mathematical models for infectious diseases;Modelos matemáticos para enfermedades infecciosas

Salud Publica de Mexico

Volumn 49, Issue 3, 2007, Pages 218-226

  Montesinos López, Osval Antonio ^a   Hernández Suárez, Carlos Moisés ^a  

^a UNIVERSIDAD DE COLIMA   (Mexico)

Author keywords

Dynamic of spread; Models for the transmission of diseases

Indexed keywords

COMMUNICABLE DISEASE; DISEASE TRANSMISSION; HUMAN; REVIEW; THEORETICAL MODEL;

COMMUNICABLE DISEASES; HUMANS; MODELS, THEORETICAL;

EID: 34250353105     PISSN: 00363634     EISSN: 16067916     Source Type: Journal    
DOI: None     Document Type: Review

References (27)

1. Ziegler P. The black death. London: Penguin, 1998.
2. Dietz K, Heesterbeek JAP. Daniel Bernoulli's epidemiological model revited. Math Biosci 2002;180:1-21.
3. Bailey NTJ.The role of Statistics in controlling and eradicating infectious diseases. Statistician 1985;34:3-17.
4. Leung PC, Ooi EE. SARS war. Combating the disease. Singapore: World Scientific Publishing, 2003.
5. Becker N. The uses of epidemic models. Biometrics 1979;35:295-305.
6. 0 in models of infectious diseases in heterogeneous populations. J Math Biol 1990;28:365-382.
7. Hernández-Suárez CM. A Markov chain approach to calculate Ro in stochastic epidemic models. J Theor Biol 2001;215:83-93.
8. Dietz K. Epidemics and Rumors: A survey. JR Stat Soc [Ser A] 1967;130(4):505-528.
9. Anderson R, May RM. Infectious diseases of humans. Oxford: Oxford University Press; 1991.
10. Diekman O, Heesterbeek JAP. Mathematical epidemiology of infectious disease: model building, analysis and interpretation. New York: John Wiley and Sons, 2000.
11. Watts DC, Strogatz SH. Collective dynamics of 'small-world' networks. Nature 1996;393:440-442.
12. Kretzschmar M, Morris M. Measures of concurrency in networks and the spread of infectious diseases. Math Biosci 1996;133:165-195.
13. Latora V, Marchiori M. Efficient behavior of small-world networks. Phys Rev Lett 2001;87(19):198701-1-198701-4.
14. Wasserman S, Faust K. Social Network Analysis: methods and aplications. Cambridge: Cambridge University Press, 1994.
15. Pastor-Satorras R, Vespignani A. Epidemic dynamics and endemic states in complex networks. Phys Rev E 2001;63:066117.
16. Barabai AL, Albert R. Emergence of scaling in random networks. Nature 1999;401:130.
17. Hernández-Suárez C, Castillo-Chávez C. Urn models and vaccine efficacy estimation. Stat Med 2000;19:827-835.
18. Wallenius KT. Biased sampling: the no central hypergeometric probability distribution. Stanford: PhD thesis, Stanford University, 1963.
19. Ball F, Lyne D. Optimal vaccination policies for stochastic epidemics among a population of households. Math Biosci 2002;177-178:303-354.
20. Riley S, Fraser C, Donnelly CA, Ghani AC, Abu-Raddad LJ, Hedley AJ, et al. Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science 2003;300:1961-1966.
21. Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, et al. Transmission dynamics and control of severe acute respiratory syndrome. Science 2003;300:1966-1970.
22. Lloyd-Smith JO, Galvani AP, Getz WM. Curtailing transmission of severe acute respiratory syndrome within a community and its hospital. Proc Biol Sci 2003;270(1528):1979-1989.
23. Hsieh YH, Chen CWS, Hsu SB. SARS outbreak, Taiwan, 2003. Emerg Infect Dis 2004;10:201-206.
24. Gumel AB, Ruan S, Day T, Watmough J, Brauer F, van den Driessche P, et al. Modelling strategies for controlling SARS outbreaks. Proc Biol Sci 2004;271(1554):2223-2232.
25. Meyers LA, Pourbohloul B, Newman ME, Skowronski DM, Brunham RC. Network theory and SARS: predicting outbreak diversity. J Theor Biol 2005;232:71-81.
26. Gjorgjieva J, Smith K, Chowell G, Sanchez F, Snyder J, Castillo-Chávez C. The role of vaccination in the control of SARS. Math Biosci Eng 2005;2(4):753-769.
27. Chowell G, Fenimore PW, Castillo-Garsow MA, Castillo-Chávez C. SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. J Theor Biol 2003;24:1-8.