The risk for a new COVID-19 wave – and how it depends on R0, 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 ), 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 , 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 and î it is shown that regions with lower R and low î may now need higher preventive measures ( p Min ) compared with other regions having higher R but also higher î , even when such immunity levels are far from herd immunity. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement T.B. and P.T. are financially supported by The Swedish Research Council ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes The details of the IRB/oversight body that provided approval or exemption for the research described are given below: The manuscript only uses mathematical models and no data. All necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines and uploaded the relevant EQUATOR Network research reporting checklist(s) and other pertinent material as supplementary files, if applicable. Yes The manuscript uses no data files.