Importance of untested infectious individuals for the suppression of COVID-19 epidemics

Francisco Perez-Reche; Norval Strachan

The posterior ( | obs ) is approximated by the empirical distribution of a set of 500 point estimates Ì‚ of the model parameters. A point estimate Ì‚ is obtained by simulating = 3000 epidemics with parameters sampled from a prior probability density Ì‚( ). In each realization, a simulation of Model 1 produces deterministic evolution functions ( ) and ( ) for the number of tested cases and cumulative deaths. The functions ( ) and ( ) are used to build a random daily time series sim ( ) = { sim ( ), sim ( )} =1 , where sim and sim are, respectively, the number of tested infected and deaths predicted at day . We assume that sim ( )~ Pois( ( )) and sim ( )~ Pois( ( )), i.e. the predicted number of tested infected and deaths are described as random variables obeying a Poisson distribution with mean ( ) and ( ), respectively. The point estimate Ì‚ is defined as the parameter vector corresponding to the realization that gives the closest prediction, sim , to the observations, obs . More explicitly, the point estimate for the model parameters is given by Ì‚= argmax { â„’( obs | sim ( ))} ,