We have updated our models for Ireland, the US and Italy to include the latest ECDC data. On the basis of our modeling assumptions, and in the absence of further closures/ measures, Italy may not see a second wave for a considerable period. Ireland may see this second wave sooner (and authorities will act to control it).
A population (whole country) based model of any country is an approximation, as there are always localized effects, especially when applied to large countries like the US. For example, cities in the North East had large first waves and are having relatively small second waves on reopening. Cities in other regions had small first waves that never really fell away and are now seeing the effects of those waves continuing to build after somewhat earlier reopening. Viewed as a whole, the US clearly has a second wave, but for the above reasons that terminology is not necessarily accurate locally.
We have included in the latest models parameters to reflect increased detection by testing (as positive test rates are reducing in many nations) and also reduced mortality as the age profile shifts. Those extra parameters add uncertainty but are necessary in order to continue to describe the evolving situation well. On the basis of the model and its prior versions referenced in previous posts, parts of the US will need to continue to take all possible measures to limit the spread of COVID-19 in order to prevent a significantly larger death toll.