Actuarial Applications of Epidemiological Models

Abstract

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.

Final outcomes and disease insurance for a controlled epidemic model

“…A key problem for the insurance is to fix the premium level to be paid by the suceptibles. This question was handled by Feng and Garrido for the deterministic general epidemic and by Lefèvre et al for the Markovian version . We are going to examine it for the more complex stochastic model .…”

Disease Spread Models to Estimate Highly Uncertain Emerging Diseases Losses for Animal Agriculture Insurance Policies: An Application to the U.S. Farm‐Raised Catfish Industry

“…DSM can allow for the inclusion of variability in the model predictions and uncertainty in the model structure and accompanying estimates used to parameterize the model, making them potentially suitable to calculate impact from ED for which knowledge is limited. DSM have been proposed to estimate disease impact for both human and livestock agricultural insurance, but have not been applied for ED insurance in specific sectors such as aquaculture. Although DSM in humans and animals share much in common, the highly stratified and confined population structure and contact network of farmed animals distinguishes DSM for animals from those for humans.…”

“…Although DSM in humans and animals share much in common, the highly stratified and confined population structure and contact network of farmed animals distinguishes DSM for animals from those for humans. Authors exploring the actuarial applications of deterministic DMS suggested that stochastic DSM could provide a more generalized and pragmatic alternative to actuarial applications …”

“…Authors exploring the actuarial applications of deterministic DMS suggested that stochastic DSM could provide a more generalized and pragmatic alternative to actuarial applications. (7) There are several examples of ED affecting aquatic animals: Taura Syndrome Virus, an infectious disease agent of shrimp, was originally transmitted to Taiwan from live shrimp imports from Ecuador in the late 1990s, and then further spread throughout Asia. (9) Koi Herpes Virus has spread in cyprinid species throughout the world due to international trade and international shows of ornamental fish.…”

Partial observer normal form for nonlinear system

“…Let us consider the well-known SIR (Susceptible, Infected, Removed) epidemic model describing the contagious disease propagation Raggett (1982);Feng and Garrido (2008) as follows:…”