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?:abstract
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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.
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