Stochastic Modelling of the COVID-19 Epidemic

The need to manage the risks related to the COVID-19 epidemic in health, economics, finance, and insurance became obvious after its outbreak. As a basis for the respective quantitative methods, this 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 and newly infected cases, and the average number of new vaccinations. The proposed model is driven by a single Brownian motion process. When fitted to COVID-19 data, it generates the observed features. It captures widely observed fluctuations in the number of newly infected cases. The fundamental probabilistic properties of the dynamics of an epidemic can be deduced from the proposed model. These can form the basis for successfully managing an epidemic and the 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 an economy during an epidemic.