×

zbMATH — the first resource for mathematics

Case fatality proportion. (English) Zbl 1281.92061
Summary: A precise definition of case fatality proportion for compartmental disease transmission models with disease induced mortality rate is given. This is applied in classical epidemic modeling frameworks to models with multiple infectious stages, with multi-groups, with spatial patches, and with age of infection. It is shown that the case fatality proportion is the sum over all stages of the product of the probability of dying from the disease at a given stage and the probability of surviving to that stage. The derived expressions for case fatality can be used to estimate the disease induced death rates from more readily available data.

MSC:
92D30 Epidemiology
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Anderson, R. M.; May, R. M., Infectious Diseases of Humans: Dynamics and Control (1991), Oxford: Oxford University Press, Oxford
[2] Anderson, R. M.; Fraser, C.; Ghani, A. C.; Donnelly, C. A.; Riley, S.; Ferguson, N. M.; Leung, G. M.; Lam, T. H.; Hedley, A. J., Epidemiology, transmission dynamics and control of SARS: the 2002-2003 epidemic, Philos. Trans. Roy. Soc. Lond. B, 359, 1091-1105 (2004)
[3] Chin, J., Control of Communicable Diseases Manual (2000), Washington: American Public Health Association, Washington
[4] Chowell, G.; Ammon, C. E.; Hengartner, N. W.; Hyman, J. W., Transmission dynamics of the great influenza pandemic of 1918 in Geneva, Switzerland: assessing the effects of hypothetical interventions, J. Theor. Biol., 241, 192-204 (2006)
[5] Day, T., On the evolution of virulence and the relationship between various measures of mortality, Proc. Roy. Soc. B, 269, 1317-1323 (2002)
[6] Dietz, K.; Heesterbeek, J. A.P., Daniel Bernoulli’s epidemiological model revisited, Math. Biosci., 180, 1-21 (2002) · Zbl 1019.92028
[7] Donnelly, C. A.; Ghani, A. C.; Leung, G. M.; Hedley, A. J.; Fraser, C., Epidemiological determinants of spread of causal agent of severe acute respiratory syndrom in Hong Kong, Lancet, 361, 1761-1766 (2003)
[8] Fung, W. K.; Yu, P. L.H., SARS case fatality rates, Can. Med. Assoc. J., 169, 4, 277-278 (2003)
[9] Guo, H.; Li, M. Y.; Shuai, Z., Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Q., 14, 259-284 (2006) · Zbl 1148.34039
[10] Horn, R. A.; Johnson, C. R., Topics in Matrix Analysis (1991), Cambridge: Cambridge University Press, Cambridge · Zbl 0729.15001
[11] Kermack, W. O.; McKendrick, A. G., A contribution to the mathematical theory of epidemics. II.—The problem of endemicity, Proc. Roy. Soc. Lond. Ser. A, 138, 55-83 (1932) · JFM 59.1190.03
[12] Webster’s New World Medical Dictionary (2003), New York: Wiley, New York
[13] Nandy, R.; Handzel, T.; Zaneidou, M.; Biey, J.; Coddy, R. Z.; Preey, R.; Strebel, P., Case-fatality rate during a measles outbreak in Eastern Niger in 2003, Clin. Infect. Dis., 42, 322-328 (2006)
[14] OIE, 2007. Update on avian influenza in animals (type h5). Technical report, World Organisation for Animal Health. URL http://www.oie.int/downld/AVIANINFLUENZA/A_AI-Asia.htm.
[15] Safan, M., Hadeler, K.P., Dietz, K., Effects of case fatality on demography. Submitted to Theor. Pop. Biol. · Zbl 1348.92152
[16] Salmani, M.; van den Driessche, P., A model for disease transmission in a patchy environment, Discret. Contin. Dyn. Syst. B, 6, 1, 185-202 (2006) · Zbl 1088.92050
[17] Thieme, H. R., Mathematics in Population Biology (2003), Princeton: Princeton University Press, Princeton · Zbl 1054.92042
[18] van den Driessche, P.; Watmough, J., Reproduction numbers and subthreadold endemic equilibria for compartmental models for disease transmission, Math. Biosci., 180, 29-48 (2002) · Zbl 1015.92036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.