Projecting the Spread of COVID19 for Germany

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

When we are interested in the number of individuals that are newly reported to be sick at some point in time t (incidences at t in short), we should not employ N 2 (t) : The change of the latter, described in (7b), is determined by the newly reported (in ‡ow) minus the out ‡ow, i.e. those that recovered (and those who died). Hence, when data provides incidences on a 13 Let us denote the expected number of individuals in state s at t by N s (t) = E 0Ñs (t) whereÑ s (t) is the stochastic process for the number of individuals in state s at t: As the expected share of individuals in state s equals the probability to be in this state, N s (t) =N = p s (t) ; we can write N s (t) = p s (t) N for the expected number of individuals in this state. Replacing the probabilities p s (t) by N s (t) would yield an ODE system in N s (t) : Our system employed for predictions below in (15) is expressed in this way.