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Stochastic Modelling of the COVID-19 Epidemic

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Abstract

The need for the management of risks related to the COVID-19 epidemic in health, economics, finance and insurance became obvious after its outbreak. As a basis for respective quantitative methods, the paper models in a novel manner the dynamics of an epidemic via a four-dimensional stochastic differential equation. Crucial time dependent input parameters include the reproduction number, the average number of externally new infected and the average number of new vaccinations. The proposed model is driven by a single Brownian motion. When fitted to COVID-19 data it generates the typically observed features. In particular, it captures widely noticed fluctuations in the number of newly infected. Fundamental probabilistic properties of the dynamics of an epidemic can be deduced from the proposed model. These form a basis for managing successfully an epidemic and related economic and financial risks. As a general tool for quantitative studies a simulation algorithm is provided. A case study illustrates the model and discusses strategies for reopening the Australian economy during the COVID-19 epidemic.

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  • Eckhard Platen, 2020. "Stochastic Modelling of the COVID-19 Epidemic," Research Paper Series 409, Quantitative Finance Research Centre, University of Technology, Sydney.
    • Handle: RePEc:uts:rpaper:409
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    File URL: https://www.uts.edu.au/sites/default/files/article/downloads/rp409.pdf
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    1. Küchler, Uwe & Platen, Eckhard, 2000. "Strong discrete time approximation of stochastic differential equations with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 54(1), pages 189-205.
    2. Sheryl L. Chang & Nathan Harding & Cameron Zachreson & Oliver M. Cliff & Mikhail Prokopenko, 2020. "Modelling transmission and control of the COVID-19 pandemic in Australia," Nature Communications, Nature, vol. 11(1), pages 1-13, December.
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    1. Ioannis Chalkiadakis & Hongxuan Yan & Gareth W Peters & Pavel V Shevchenko, 2021. "Infection rate models for COVID-19: Model risk and public health news sentiment exposure adjustments," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-39, June.

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    More about this item

    Keywords

    stochastic epidemic model; stochastic differential equations; squared Bessel process; COVID-19 epidemic; simulation;
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