The risk for a new COVID-19 wave – and how it depends on R ₀ , the current immunity level and current restrictions

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 î 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 , î 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 î plays a more influential roll than when immunity is obtained from vaccination. Secondly, by comparing regions with different R ₀ and î it is shown that regions with lower R ₀ and low î may now need higher preventive measures ( p _Min ) compared with other regions having higher R ₀ but also higher î , even when such immunity levels are far from herd immunity.