SARS-CoV-2 waves in Europe: A 2-stratum SEIRS model solution

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Levan Djaparidze (E.E., B.C.S.), Federico Lois (B.C.S.)

Abstract In order to design actionable SARS-CoV-2 strategies, we extended the SEIRS model to support stratified isolation levels for healthy <60 and vulnerable individuals. At first, we forced isolation levels to be uniform, showing that daily deaths curves of all metropolitan areas in the analysis can be fitted using homogeneous Ro=3.3. In the process, we established the possibility that an extremely short infectiousness period of 2 days coupled with 5 days exposure may be responsible for the multiple deaths valleys observed during the weeks following lockdowns.

Regardless of the infectiousness period, we realized that is possible to infer non-uniform isolation levels for healthy <60 and vulnerable by forcing the model to match the <60 to >60 age serology ratio reported in seroprevalence studies. Since the serology ratio is more robust than absolute values, we argue immunity level estimations made in this way (Madrid 41%; Catalonia 23%; Brussels 70%; and Stockholm 62%) are closer to reality.

In locations where we didn’t find reliable serology, we performed immunity estimations assuming Spain’s serology ratio (Paris: 23%; London: 33%). We predict that, with the exception of Brussels, no location can return to normal life without having a second wave (albeit in Stockholm a smaller one). For locations far from the herd immunity threshold (HIT) we searched what isolation values allow to return to normal life in 90 days minimizing final deaths, shockingly all found isolations for healthy <60 were negative (i.e. coronavirus parties minimize final deaths).

Then, assuming an ideal 1-day long vaccination campaign with a 77% efficacy vaccine, we compared predicted final deaths of those 90-day strategies for all possible vaccination dates with a 180-day long vaccine waiting strategy that imposes 0.40 mandatory isolation to healthy <60 and results in 0.65 isolation to vulnerable.

We found that 180-day of mandatory isolations to healthy <60 (i.e. schools and workplaces closed) produces more final deaths if the vaccination date is later than (Madrid: Feb 23 2021; Catalonia: Dec 28 2020; Paris: Jan 14 2021; London: Jan 22 2021). We also modeled how average isolation levels change the probability of getting infected for a single individual that isolates differently than average.

That led us to realize disease damages to third parties due to virus spreading can be calculated and to postulate that an individual has the right to avoid isolation during epidemics (SARS-CoV-2 or any other) if these damages can be covered with a novel proposed isolation exemption insurance policy.

Finally we conclude that our 2-stratum SEIRS model is suitable to predict SARS-CoV-2 epidemic behavior and can be used to minimize covid-19 disease and isolations related damages. To the sole effect of understanding and verifying its content the same model used through this paper has been made available online at