Discrete epidemic models

Mathematical Biosciences and Engineering

Volumn 7, Issue 1, 2010, Pages 1-15

  Brauer, Fred ^a,b   Feng, Zhilan ^a,c   Castillo Chavez, Carlos ^a,d  

^a ARIZONA STATE UNIVERSITY   (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^c PURDUE UNIVERSITY   (United States)

^d SANTA FE INSTITUTE   (United States)

Author keywords

Continuous time epidemic models; Discrete epidemic models; Epidemic; Final size; Single outbreak

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; COMMUNICABLE DISEASE; DISEASE COURSE; EPIDEMIC; HUMAN; INFLUENZA; INFLUENZA VIRUS A H1N1; METHODOLOGY; PUBLIC HEALTH; SARS CORONAVIRUS; SEVERE ACUTE RESPIRATORY SYNDROME;

COMMUNICABLE DISEASES; DISEASE OUTBREAKS; DISEASE PROGRESSION; HUMANS; INFLUENZA A VIRUS, H1N1 SUBTYPE; INFLUENZA, HUMAN; MODELS, BIOLOGICAL; PUBLIC HEALTH; SARS VIRUS; SEVERE ACUTE RESPIRATORY SYNDROME;

EID: 77149155137     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2010.7.1     Document Type: Article

References (30)

1. L. J. S. Allen, Some discrete-time SI, SIR, and SIS epidemic models, Math. Biosci., 124 (1994), 83-105.
2. L. J. S Allen, "An Introduction to Mathematical Biology," Prentice-Hall, 2007.
3. L. J. S. Allen and A. M. Burgin, Comparison of deterministic and stochastic SIS and SIR models in discrete time, Math. Biosci., 163 (2000), 1-33.
4. L. J. S. Allen, M. A. Jones and C. F. Martin, A discrete-time model with vaccination for a measles epidemic, Math. Biosci., 105 (1991), 111-131.
5. R. M. Anderson and R. M. May, "Infectious Diseases of Humans," Oxford Science Publications, Oxford, 1991.
6. J. Arino, F. Brauer, P. van den Driessche, J. Watmough and J. Wu, Simple models for containment of a pandemic, J. Roy. Soc. Interface, 3 (2006), 453-457.
7. N. T. J. Bailey, "The Mathematical Theory of Infectious Diseases," Hafner, New York, second ed., 1975.
8. L. M. A. Bettencourt, R. M. Ribeiro, G.Chowell, T. Lant and C. Castillo- Chavez, Towards real time epidemiology: Data assimilation, modeling and anomaly detection of health surveillance data streams, in "Intelligence and security informatics: Biosurveillance" (G.D. Zeng, K. Komatsu, C. Lynch,Eds.), Proceedings of the 2nd NSF Workshop, Biosurveillance, Lecture Notes in Computer Science, New Brunswick, NJ Springer-Verlag (2007), 79-90.
9. F. Brauer, Age-of-infection and the final size relation, Math. Biosc. and Eng., 5 (2008), 681-690.
10. F. Brauer and C. Castillo-Chavez, "Mathematical Models in Population Biology and Epidemiology," Springer-Verlag, 2001.
11. C. Castillo-Chavez and A-A. Yakubu, Dispersal, disease and life-history evolution, Math. Biosci., 173 (2001), 35-53.
12. C. Castillo-Chavez and A-A. Yakubu, Discrete-time S-I-S models with complex dynamics, Nonlinear Analysis, 47 (2001), 4753-4762.
13. C. Castillo-Chavez and A-A. Yakubu, Discrete-time S-I-S models with simple and complex population dynamics, in "Mathematical Approaches for Emerging and Reemerging Infectious Diseases" (eds., C. Castillo-Chavez, et al.), Springer-Verlag, IMA, 125 (2001), 153-163.
14. G. Chowell, P.W. Fenimore, M. A. Castillo-Garsow and C. Castillo-Chavez, SARS outbreaks in Ontario, Hong Kong, and Singapore: the role of diagnosis and isolation as a control mechanism, J. Theor. Biol., 224 (2003), 1-8.
15. Z. Feng, Final and peak epidemic sizes for SEIR models with quarantine and isolation, Math. Biosc. and Eng., 4 (2007), 675-686.
16. N. M. Ferguson, D. A. T. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn and D. S. Burke, Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature, 437 (2005), 209-214.
17. N. M. Ferguson, D. A. T. Cummings, C. Fraser, J. C. Cajka, P. C. Cooley and D. S. Burke, Strategies for mitigating an influenza pandemic, Nature, 442 (2006), 448-452.
18. T. C. Germann, K. Kadau, I. M. Longini and C. A.Macken, Mitigation strategies for pandemic influenza in the United States, Proc. Nat. Acad. Sci., 103 (2006), 5935-5940.
19. A. Gumel, S. Ruan, T. Day, J. Watmough, P. van den Driessche, F. Brauer, D. Gabrielson, C. Bowman, M. E. Alexander, S. Ardal, J. Wu and B. M. Sahai, Modeling strategies for controlling SARS outbreaks based on Toronto, Hong Kong, Singapore and Beijing experience, Proc. Roy. Soc. London, 271 (2004), 2223-2232.
20. H. W. Hethcote, The mathematics of infectious diseases, SIAM Review, 42 (2000), 599-653,
21. J. M. Hyman, J. Li and E. A. Stanley, The differential infectivity and staged progression models for the transmission of HIV, Math. Biosci., 155 (1999), 77-109.
22. J. M. Hyman and J. Li, Infection-age structured epidemic models with behavior change or treatment, J. Biol. Dyn., 1 (2007), 109-131.
23. W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. London, 115 (1927), 700-721.
24. J. Li, Z. Ma and F. Brauer, Global analysis of discrete-time SI and SIS epidemic models, Math. Biosc. and Eng., 4 (2007), 699-710.
25. I. M. Longini, M. E. Halloran, A. Nizam and Y. Yang, Containing pandemic influenza with antiviral agents, Am. J. Epidem., 159 (2004), 623-633.
26. I. M. Longini, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakul, D. T. Cummings and M. E. Halloran, Containing pandemic influenza at the source, Science, 309 (2004), 623-633.
27. J. Ma and D. J. D. Earn, Generality of the final size formula for an epidemic of a newly invading infectious disease, Bull. Math. Biol., 68 (2006), 679-702.
28. S. Riley, 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, S-V Lo, P-Y Leung, T. Tsang, W. Ho, K-H Lee, E. M. C. Lau, N. M. Ferguson and R. M. Anderson, Transmission dynamics of the etiological agent of SARS in Hong Kong: Impact of public health interventions, Science, 300 (2003), 1961-1966.
29. 0 for age-of-infection models, Math. Biosc. and Eng., 5 (2008), 585-599.
30. Y. Zhou, Z. Ma and F. Brauer, A discrete epidemic model for SARS transmission and control in China, Math. and Computer Modelling, 40 (2004), 1491-1506.