Abstract
In this paper, we aim to determine an optimal insurance premium rate for health-care in deterministic and stochastic SEIR models. The studied models consider two standard SEIR centres characterised by migration fluxes and vaccination of population. The premium is calculated using the basic equivalence principle. Even in this simple set-up, there are non-intuitive results that illustrate how the premium depends on migration rates, the severity of a disease and the initial distribution of healthy and infected individuals through the centres. We investigate how the vaccination program affects the insurance costs by comparing the savings in benefits with the expenses for vaccination. We compare the results of deterministic and stochastic models.
Highlights
Epidemics cause severe damage to social welfare and can result in a massive loss of working days
Modern epidemiology is a consistent theory that provides a variety of models, and the tool-kit to study the dependencies of the solutions from their parameters and the initial conditions
The theory shows that the solution offered by a stochastic model, with a lot of time steps, is approaching the solution to a dynamic problem with initial conditions in terms of fractions of initially infected population
Summary
Epidemics cause severe damage to social welfare and can result in a massive loss of working days. One of the most fundamental works with strict mathematical and medical approaches is [10] Investigation of these models can help understanding the key points of the phenomena and determine the optimal vaccination strategy, which could stop the spread of the pandemic and reduce the economic costs. The aim of this work is to investigate the optimal health-care premium rate π in deterministic and stochastic connected SEIR centres. We consider different scenarios (different centres’ characteristics), investigate the dependence of premium π on the amount of vaccine available, infection rates, migration intensities, sizes of population and vaccine allocation strategies. We consider deterministic and stochastic SEIR models with two connected centres and constant migration fluxes. We calculate the health-care premium rate for different parameters of the model by optimally (in some sense) allocating the vaccine among the centres. In Appendix A we calculate the reproduction number for two connected SEIR centres
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