## Actuarial applications of epidemiological models.(English)Zbl 1213.91089

Summary: The risk of a global avian flu or influenza A (H1N1) pandemic and the emergence of the worldwide SARS epidemic in 2002–2003 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 goes only so far in setting up epidemiological models that better reflect the transmission dynamics. This paper attempts to build a bridge between epidemiological and actuarial modeling and set up an actuarial model that 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.

### MSC:

 91B30 Risk theory, insurance (MSC2010) 92D30 Epidemiology 62P05 Applications of statistics to actuarial sciences and financial mathematics 62P10 Applications of statistics to biology and medical sciences; meta analysis

Maple; Matlab
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### References:

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