PDF
Abstract
The age of infection approach introduced by Kermack and Mckendrick in 1927 gives a unified way of describing and analyzing a variety of epidemic models, including models with multiple stages, treatment, and heterogeneous mixing. The author gives a description of the main results for such models, emphasizing the use of the final size relation to estimate the size of the epidemic.
Keywords
Epidemic models
/
Treatment models
/
Basic reproduction number
/
Final size relation
Cite this article
Download citation ▾
Fred Brauer.
General compartmental epidemic models.
Chinese Annals of Mathematics, Series B, 2010, 31(3): 289-304 DOI:10.1007/s11401-009-0454-1
| [1] |
ArinoJ., BrauerF., van den Driessche, et al.. A final size relation for epidemic models. Math. Biosc. Eng., 2007, 4: 159-176
|
| [2] |
ArinoJ., BrauerF., van den Driessche, et al.. Simple models for containment of a pandemic. J. Roy. Soc. Interface, 2006, 3: 453-457
|
| [3] |
BrauerF.. Age-of-infection and the final size relation. Math. Biosc. Eng., 2008, 5: 681-690
|
| [4] |
BrauerF., WatmoughJ.. Age of infection epidemic models with heterogeneous mixing. J. Biol. Dyn., 2009, 3: 324-330
|
| [5] |
DiekmannO., HeesterbeekJ. A. P.Mathematical Epidemiology of Infectious Diseases, 2000, Chichester, Wiley
|
| [6] |
DiekmannO., HeesterbeekJ. A. P., MetzJ. A. J.. On the definition and the computation of the basic reproductive ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol., 1990, 28: 365-382
|
| [7] |
DietzK.AndersonR. M., MayR. M.. Overall patterns in the transmission cycle of infectious disease agents, Population Biology of Infectious Diseases. Life Sciences Research Report, 25, 1982, Berlin, Heidelberg, New York, Springer-Verlag: 87-102
|
| [8] |
ErdösP., RényiA.. On random graphs. Publicationes Mathematicae, 1959, 6: 290-297
|
| [9] |
ErdösP., RényiA.. On the evolution of random graphs. Pub. Math. Inst. Hung. Acad. Science, 1960, 5: 17-61
|
| [10] |
ErdösP., RényiA.. On the strengths of connectedness of a random graph. Acta Math. Scientiae Hung., 1961, 12: 261-267
|
| [11] |
FengZ.. Final and peak epidemic sizes for SEIR models with quarantine and isolation. Math. Biosc. Eng., 2007, 4: 675-686
|
| [12] |
FengZ., XuD., ZhaoW.. Epidemiological models with non-exponentially distributed disease stages and applications to disease control. Bull. Math. Biol., 2007, 69: 1511-1536
|
| [13] |
GumelA., RuanS., DayT., et al.. Modeling strategies for controlling SARS outbreaks based on Toronto, Hong Kong, Singapore and Beijing experience. Proc. Roy. Soc. London, 2004, 271: 2223-2232
|
| [14] |
HeesterbeekJ. A. P., MetzJ. A. J.. The saturating contact rate in marriage and epidemic models. J. Math. Biol., 1993, 31: 529-539
|
| [15] |
HeffernanJ. M., SmithR. J., WahlL. M.. Perspectives on the basic reproductive ratio. J. Roy. Soc. Interface, 2005, 2: 281-293
|
| [16] |
HymanJ. M., LiJ.. Infection-age structured epidemic models with behavior change or treatment. J. Biol. Dyn., 2007, 1: 109-131
|
| [17] |
HymanJ. M., LiJ., StanleyE. A.. The differential infectivity and staged progression models for the transmission of HIV. Math. Biosci., 1999, 155: 77-109
|
| [18] |
KermackW. O., GMcKendrickA. G.. A contribution to the mathematical theory of epidemics. Proc. Royal Soc. London, 1927, 115: 700-721
|
| [19] |
LloydA. L.. Realistic distributions of infectious periods in epidemic models: changing patterns of persistence and dynamics. Theor. Pop. Biol., 2001, 60: 59-71
|
| [20] |
Mena-LorcaJ., HethcoteH. W.. Dynamic models of infectious diseases as regulators of population size. J. Math. Biol., 1992, 30: 693-716
|
| [21] |
NewmanM. E. J.. The spread of epidemic disease on networks. Phys. Rev. E, 2002, 66: 016128
|
| [22] |
NewmanM. E. J.. The structure and function of complex networks. SIAM Review, 2003, 45: 167-256
|
| [23] |
NewmanM. E. J., StrogatzS. H., WattsD. J.. Random graphs with arbitrary degree distributions and their applications. Phys. Rev. E, 2001, 64: 026118
|
| [24] |
NoldA.. Heterogeneity in disease transmission modeling. Math. Biosc., 1980, 52: 227-240
|
| [25] |
RileyS., FraserC., DonnellyC. A., et al.. Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science, 2003, 300: 1961-1966
|
| [26] |
StrogatzS. H.. Exploring complex networks. Nature, 2001, 410: 268-276
|
| [27] |
WearingH. J., RohaniP., KeelingM. J.. Appropriate models for the management of infectious diseases. PLOS Medicine, 2005, 2: 621-627
|
| [28] |
YangC. K., BrauerF.. Calculation of R0 for age-of-infection models. Math. Biosc. Eng., 2008, 5: 585-599
|
RIGHTS & PERMISSIONS
Editorial Office of CAM (Fudan University) and Springer Berlin Heidelberg