A Divide and Conquer Strategy against the Covid-19 Pandemic?!

The concern about (socio-)economic consequences of collective lockdowns in the Covid-19 pandemic calls for alternative strategies. We consider adivide and conquer strategyin which a high risk group (HRG) is put on strict isolation, whereas the remainder of the population is exposed to the virus, building up immunity against Covid-19. The question is whether this strategy may suppress the effective reproduction number below the critical value of<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20092155v1_inline1.gif"/></alternatives></inline-formula>without further lockdown once the HRG is released from isolation. While this proposal appears already rather academic, we show that<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20092155v1_inline2.gif"/></alternatives></inline-formula>can only be obtained provided that the HRG is less than ~ 20 − 30% of the total population. Hence, this strategy is likely to fail in countries with a HRG larger than the given upper bound. In addition, we argue that the maximum infection rate occurring in this strategy is likely to exceed realistic capacities of most health care systems. While the conclusion is rather negative in this regard, we emphasise that the strategy ofstopping the curveat an early stage of the Covid-19 pandemic has a chance to work out. The required duration of the lockdown is estimated to be τ ~ 14 days/<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20092155v1_inline3.gif"/></alternatives></inline-formula>(up to some order one factor) for<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20092155v1_inline4.gif"/></alternatives></inline-formula>, provided a systematic tracing strategy of new infections exists for the subsequent relaxation phase. In this context we also argue why<inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="20092155v1_inline5.gif"/></alternatives></inline-formula>remains the crucial parameter which needs to be accurately monitored and controlled.