# Insurance Model to Estimate the Financial Risk Due to Direct Medical Cost on Dengue Outbreaks

• S. S. N. Perera
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)

## Abstract

Dengue fever is among the most critical infectious disease in tropical and subtropical countries of the world, and represents a significant financial and disease burden in endemic regions. In recent decades, it is observed that significant increase in the recorded infected cases and hence an increase in the public health burden. Mathematical models with modern financial features have become invaluable management tools for epidemiologists, both to understand the underlying observed dynamics as well as making quantitative predictions of the disease spared risk and how such a risk depends on the effectiveness of different control measures. This chapter is an attempt to build a bridge between epidemiological and insurance modeling and set up an actuarial based tool that provides financial arrangements to cover the future medical expenses resulting from the medical treatments of dengue disease. Dynamics of the Dengue transmission can be expressed using classical compartment Susceptible, Infected and Recovered (SIR) model. Introducing the fractions of the compartment of the host population as probability densities, we convert classical SIR model into probability model. Taking fractions as probability densities, we then develop the insurance plan to cover the future financial burden due to direct medical expenses. The premium, the present financial burden due to future expenses is defined via the equivalence principle and sensitivity of it with respect to model parameters and external variables is discussed. By introducing several control measures, the variability of the present financial burden with respect to such measurers are discussed. Further, the efficiency of the controls are analyzed. By defining the reserve function, necessary and sufficient criterion for the existence of insurance plans is also discussed.

## Keywords

Dengue Dynamical system Expected value Equivalence principle Actuarial evaluation

## AMS Subject Classification:

34D20 92B05 92D30

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