Projecting the Spread of COVID19 for Germany

Jean Roch Donsimoni; Rene Glawion; Bodo Plachter; Klaus Waelde

Why should economists work on an epidemic? The economic costs of COVID-19 are huge and seem to be larger than those of the …nancial crisis starting in 2007. 4 This paper provides a model that allows to understand the spread of the disease. We employ a model in the tradition of search and matching models originating from Diamond (1982) , Mortensen (1982) and Pissarides (1985) . The basic structure of these models (continuous time Markov chains) is identical to epidemiological models (as becomes clear very quickly when reading overviews like e.g. Hethcote, 2000) . Compared to standard search and matching models, we do allow for four states, however. We extend the typical matching framework from a technical perspective by taking the stochastic nature of transitions and their prediction for the probability to be in various states into account. These probabilities are described by forward Kolmogorov equations. As we work with a discrete number of states, we obtain an ordinary di¤erential equation system. 5 The conclusion discusses various next steps that should be undertaken to understand economic consequences of COVID-19 better. We believe that our framework can form the basis for an understanding of economic costs of the pandemic.