  The COVID-19 pandemic has hit different parts of the world differently: some
regions are still in the rise of the first wave, other regions are now facing a
decline after a first wave, and yet other regions have started to see a second
wave. The current immunity level $\hat i$ in a region is closely related to the
cumulative fraction infected, which primarily depends on two factors: a) the
initial potential for COVID-19 in the region (often quantified by the basic
reproduction number $R_0$), and b) the timing, amount and effectiveness of
preventive measures put in place. By means of a mathematical model including
heterogeneities owing to age, social activity and susceptibility, and allowing
for time-varying preventive measures, the risk for a new epidemic wave and its
doubling time, and how they depend on $R_0$, $\hat i$ and the overall effect of
the current preventive measures, are investigated. Focus lies on quantifying
the minimal overall effect of preventive measures $p_{Min}$ needed to prevent a
future outbreak. The first result shows that the current immunity level $\hat
i$ plays a more influential roll than when immunity is obtained from
vaccination. Secondly, by comparing regions with different $R_0$ and $\hat i$
it is shown that regions with lower $R_0$ and low $\hat i$ may now need higher
preventive measures ($p_{Min}$) compared with other regions having higher $R_0$
but also higher $\hat i$, even when such immunity levels are far from herd
immunity.
