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The risk of a global avian flu or influenza A (H1N1) pandemic, and the emergence of the worldwide SARS epidemic in 2002–03 have led to a revived interest in the study
of infectious diseases. Mathematical models have become important tools in analyzing the transmission dynamics and in measuring the effectiveness of controlling strategies.
Research on infectious diseases in the actuarial literature only goes so far as to set up epidemiological models which better reflect the transmission dynamics. This paper
attempts to build a bridge between epidemiological and actuarial modeling and set up an actuarial model which provides financial arrangements to cover the expenses
resulting from the medical treatments of infectious diseases.
Based on classical epidemiological compartment models, the first part of this paper proposes insurance policies and models to quantify the risk of infection and formulates
financial arrangements, between an insurer and insureds, using actuarial methodology. For practical purposes, the second part employs a variety of numerical methods to
calculate premiums and reserves. The last part illustrates the methods by designing insurance products for two well known epidemics: the Great Plague in England and the SARS epidemic in Hong Kong.
|Divisions:||Concordia University > Faculty of Arts and Science > Mathematics and Statistics|
|Item Type:||Monograph (Technical Report)|
|Authors:||Feng, Runhuan and Garrido, José|
|Series Name:||Department of Mathematics & Statistics. Technical Report No. 6/08|
|Corporate Authors:||Concordia University. Department of Mathematics & Statistics|
|Keywords:||epidemiological compartment models; SIR model; actuarial mathematics; infectious diseases; health insurance; Runge–Kutta method; ratemaking; reserves.|
|Deposited By:||DIANE MICHAUD|
|Deposited On:||02 Jun 2010 12:02|
|Last Modified:||08 Dec 2010 18:19|
Anderson, Roy M. and May, Robert M. (1991). Infectious Diseases of Humans. Oxford: Oxford University Press.
Barnes, Belinda and Fulford, Glenn Robert (2008). Mathematical Modelling with Case Studies: A Differential Equations Approach using Maple and MATLAB, 2nd Ed.
Boca Raton: Chapman & Hall/CRC.
Boyce, William E. and DiPrima, Richard C. (1986). Elementary Differential Equations and Boundary Value Problems. 4th Ed. New York: John Wiley and Sons.
Bowers, Newton L., Gerber, Hans U., Hickman, James C., Jones, Donald A. and Nesbitt Cecil J. (1997). Actuarial Mathematics. Chicago: The Society of Actuaries.
Brauer, Fred and Castillo-Ch´avez, Carlos (2001). Mathematical Models in Population Biology and Epidemiology. Springer–Verlag New York.
Chen, Hua and Cox, Samuel H. (2007). An option–based operational risk management on pandemics. Actuarial Research Clearing House. 2008.1: 1–27.
CIA (2009), Considerations for the development of a pandemic scenario. Canadian Institute of Actuaries. Committee on Risk Management and Capital Requirements. Research Paper 209095.
Chowell, Gerardo, Fenimore, Paul W., Castillo–Garsow, Mellisa A. and Castillo–Chàvez, Carlos (2003). SARS outbreaks in Ontario, Hong Kong and Singapore: the role of diagnosis and isolation as a control mechanism. Journal of Theoretical Biology. 224: 1–8.
Coombes, Kevin R., Hunt, Brian R., Lipsman, Ronald L., Osborn, John E. and Stuck Garrett J. (1997). Differential Equations with Maple. 2nd Ed. New York: John
Wiley and Sons.
Cornall, Monica, Chan, Margaret and Sparks Jan (2003). UK vaccination programme risk and reward. The Staple Inn Actuarial Society. London.
Hethcote, Herbert W., Stech, Harlan W. and van den Driessche,Pauline(1981). Periodicity and stability in epidemics models: A survey, in Differential Equations and Applications in Ecology, Epidemics and Population Problems. New York: Academic Press, 65–82.
Hethcote, Herbert W. (2000). The mathematics of infectious diseases. Society for Industrial and Applied Mathematics Review. 42(4): 599–653.
Hoem, Jan M. (1988). The versatility of the Markov chain as a tool in the mathematics of life insurance. Record of Proceedings, International Congress of Actuaries. Helsinki, Finland. 171–202.
Jia, Na, Tsui, Lawrence (2005). Epidemic modelling using SARS as a case study. North American Actuarial Journal . 9(4): 28–42.
Jones, Bruce L. (1994). Actuarial calculations using a Markov model. Transactions of the Society of Actuaries. XLVI: 227–250.
Mäkinen, Mika (2009). Pandemic. International Actuarial Association. Task Force on Mortality. http://www.actuaries.org/CTTEES TFM/Documents/Pandemic Makinen EN.pdf
Mollison, Denis, Isham, Valerie and Grenfell, Bryan T. (1994). Epidemics: models and data. Journal of Royal Statistical Society A. 157(Part 1): 115–149.
Raggett, Graham F. (1982). Modeling the Eyam plague. Bulletin of the Institute of Mathematics and its Applications. 18: 221–226.
Stracke, Andrea and Heinen, Winfried (2006). Influenza pandemic: The impact on an insured lives life insurance portfolio. The Actuary Magazine. June.
Waters, Howard R. (1984). An approach to the study of multiple state models. Journal of the Institute of Actuaries. 111(Part II): 611–624.
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