| Popis: |
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. |
