Using standard systems biology methodology we generated a dynamic model, which should apply to various geographical units after adjustment to the population size. We use the term ‘geographical unit’ for an area where the lockdown intensity is fairly homogeneous. This may be a country, a state, or even a city or village. For each of the processes depicted in Fig. 1, the model uses a chemical reaction equation (describing the conversion that occurs in the process) and a rate equation (describing the rate at which this occurs in terms of a rate ‘constant’ [inverse probability] and concentrations of species (such as infected-non-tested indivudals)).
For the unmanaged epidemic, 3 % of the population is computed to die from COVID-19 infection within 3 months (red line in Fig. 2B). A ‘complete shutdown’ at t=15 days into the epidemic (modelled as a permanent reduction of infection probability by a factor of 10 through a ‘social distancing factor’ [see below] of 10) should keep the percentage of deceased individuals down to 0.003 % (400 times lower than the natural death rate per year; purple line in Fig. 2B). In our model simulations, a less complete lockdown increased lethality in a highly nonlinear way (Fig. 3). Dividing the fraction of the population that becomes infected, by the fraction deceased, both as shown in Fig. 3, we obtained a proportionality constant independent of the intensity of the lockdown, and equal to 27 (which reflects the inverse of the lethality of the disease). Consequently, in order to achieve the 50 % herd immunity that should quench this and a subsequent wave of the epidemic, one would have to accept a death rate of 2 % over some 5 months. This corresponds to approximateley three times the natural death rate: adjusting the lockdown intensity so as to obtain sufficient herd immunity may thereby be unacceptable ethically.
Acceptable strategies should perhaps focus on measures that keep the death toll around 0.03 %/year, i.e. well below the natural death rate. Because the terminally ill occupy an intensive care bed for approximately a month with half of them surviving, and assuming a peak of the epidemic lasting 3 months (see below), this corresponds to approximately 2 such beds for every 10 000 inhabitants, close to the actual total intensive care capacities in Northern Europe. The blue line in Figure 3 shows the computed COVID-19 mortality as a function of the intensity of the lockdown. The lockdown intensity is parameterized by the ‘social distancing factor’ which we define as the factor decrease in infection coefficient (Fig. 1) brought about by the lockdown measure called by the government of the geographical unit. A 2.5 fold permanent reduction in social interactions (i.e. a social distancing factor of 2.5) should reduce COVID-19 mortality from 3 % to this 0.03 % (the blue line in Fig. 3). However, the duration of the epidemic (measured as the half rise time) varies appreciably with the social distance. Around a 2.2 fold increase in social distance the duration of the epidemic is predicted to be the longest (more than half a year, see the grey line in Fig.3 at social distancing factor of 2.2). This has the benefit of minimizing the challenge on the intensive care unit capacity, but may well increase the economic damage.
A full lockdown should reduce the duration of the epidemic to 25 days (0.8 months, see grey line in Fig. 3), with a stronger but short effect on the economy (but see below for an extra strategy that will be needed to prevent re-emergence of the epidemic). On the other hand, a 3-fold decrease in social contact (i.e. implementation of a lockdown with an intensity of a social distancing factor of 3) should already reduce the duration to 40 days (1.3 months, grey line in Fig. 3), with as additional benefit a much reduced lethality (0.008% compared with 0.5 at a 2.2 fold reduction of infection probability; blue line in Fig. 3) and much reduced economic damage when compared to the situation of a social distancing factor of 2.2). From this we conclude that a soft lockdown such as corresponding to a 2.2 fold reduction in social interaction could be the worst strategy to follow, that a stronger lockdown is advisable and that that lock down need not be that much stronger (e.g. a social distancing factor of 3 rather than 2.2 should do; see Fig. 3)). It should be noted that in all these cases the herd immunity reached within a year will not suffice to prevent a second wave of epidemic.
A strong lockdown is hardship. Therefore we examined whether such a lockdown could be intermitted with periods with normal social contact, without endangering the success of the strategy. We found (Fig. 4A) that a 55%-on-45%-off schedule for the full lockdown will not suppress the epidemic. In order to suppress the SARS-CoV-2 virus, two thirds of the time society should be locked down, leaving one third for social interactions (Fig. 4B and supplementary material Fig. S1). This seems an attractive alternative to a permanent lockdown provided a selection of economic activities that require live human-human interactions could be confined to shorter time periods without increasing contact intensity.
A more complex strategy should be one where the intensity of the shutdown is adapted on the fly to the severity of the epidemic. Choosing the fraction of the population that is newly tested as virus-positive (blue line in Fig. 5) as the variable controlling the social distancing factor as shown by the orange line in and legend to Fig. 5, this adaptive strategy should do better than a fixed lockdown of comparable intensity. Implemented at time 15 days after the first detection of an infected individual, this should lead to a lethality after one year of only 0.013 % (grey line in Fig. 5), i.e. one fourth the 0.33 % a continuous 2.25 fold lockdown would have led to (see Fig. 3). A disadvantage of this adaptive strategy is that the mortality increases linearly with time also after the first year. However, the total mortality should still not overtake that of the constant lockdown by social distancing factor of 2.25 until after 10 years. We reckon that long before then a vaccine, some other cure, or an improved patient detection and insulation strategy should have been discovered and put in place. The adaptive lockdown could be optimized further in terms of parameters and with respect to any specific epidemic, culture and geographical unit.
The blue line in Figure 5 shows that for this adaptive strategy the effect on the number of individuals tested positively should be noticeable immediately after its onset: initially at least, the strategy comes with a rather intensive lockdown, much stronger than what many governments are practicing judging by the slower rate of decrease in percentage infected reported for Europe and North America . Most governments do the inverse: they exercise a soft lockdown first, increasing the lockdown intensity subsequently (see also below). The adaptive lockdown strategy proposed here begins with a harsh lockdown to then relax it. The latter is the one that should work.
One of the important determinants of the success of a lockdown is how early in the epidemic it is enforced. This is even so for the adaptive lockdown strategy. Should the strategy be enacted 15 days later than modelled here, the number of dead at the end of the year would become 20 times higher and the required initial lockdown intensity should become 500 (in terms of social distancing factor), even though ultimately the adapting lockdown level should subside to the same social distancing factor of 2.2. So, governments should act earlier rather than later.
This phenomenon is reinforced by comparing a ‘soft-then-strong’ lockdown strategy that starts with a mild lockdown and is then followed by a harsh lockdown, to an inverse strategy, i.e. first harsh and then mild. Fig. 6 shows that the effects of the two strategies differ immensely: for social distancing factors of 2 and 10 for instance, the harsh-then-soft lockdown leads to a lethality of 0.003% whereas 0.9 % of the population would die from the corresponding soft-then-harsh strategy.
Faster testing of the symptomatic individuals should have little effect (results not shown), but a faster detection of symptoms in the individuals that have been infected but are not yet symptomatic should be highly effective: Doubling this rate constant reduces lethality after one year from 0.013 % to 0.0030 % and reduces the required peak in the adapting social distancing factor to only 1.4, thereby strongly reducing the economic damage). Quadrupling the same rate constant reduces the distancing to a factor smaller than 1.1 and the % deceased after a year to 0.00012 %. This same method should help detecting people that import the disease virus from abroad. Quarantine of the newly arrived persons should be effective, but should the entry of the infected people not be noticed, then the adaptive strategy should take care of it provided there is testing (results not shown): in the adaptive strategy the number of infected individuals is closely related to the control variable of the adaptive system.
An attractive alternative to the adaptive strategy is the full lockdown until virus extinction. Here the lockdown strategy must be intensive and continued until there are no infected people left in the population (results not shown). However, this strategy is sensitive to import of new infections (Figure S2) and should only be robust if an adaptive strategy serves as back up.
The adaptive strategy does have the disadvantage that it should be maintained until a vaccine, or a much faster detection method of the infections, or another effective way of reducing the infection coefficient, has arrived. Stopping the adaptive control at 180 days after onset, had the effect that the epidemic re-emerged with a half rise at 230 days, i.e. only one and a half month later (Fig. S3). The adaptive control method is ill-compatible with the extinction strategy however, as in the latter there is no live control variable left. Yet the adaptive strategy can be used as back up, provided a suitable and fast control variable is identified.