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The COVID-19 pandemic has hit different parts of the world differently: someregions are still in the rise of the first wave, other regions are now facing adecline after a first wave, and yet other regions have started to see a secondwave. The current immunity level $\hat i$ in a region is closely related to thecumulative fraction infected, which primarily depends on two factors: a) theinitial potential for COVID-19 in the region (often quantified by the basicreproduction number $R_0$), and b) the timing, amount and effectiveness ofpreventive measures put in place. By means of a mathematical model includingheterogeneities owing to age, social activity and susceptibility, and allowingfor time-varying preventive measures, the risk for a new epidemic wave and itsdoubling time, and how they depend on $R_0$, $\hat i$ and the overall effect ofthe current preventive measures, are investigated. Focus lies on quantifyingthe minimal overall effect of preventive measures $p_{Min}$ needed to prevent afuture outbreak. The first result shows that the current immunity level $\hati$ plays a more influential roll than when immunity is obtained fromvaccination. 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 higherpreventive measures ($p_{Min}$) compared with other regions having higher $R_0$but also higher $\hat i$, even when such immunity levels are far from herdimmunity.

The risk for a new COVID-19 wave -- and how it depends on $R_0$, the current immunity level and current restrictions