Evaluation of the potential incidence of COVID-19 and effectiveness of contention measures in Spain: a data-driven approach

Alberto Aleta; Yamir Moreno

days, the epidemic is greatly reduced. As a matter of fact, it has been recently reported [13] that this average number of days went down in China from 4.4 days at the beginning of the outbreak to 2.6 days, which is one of the reasons invoked to explain why the epidemic has started to decline in mainland China. In our case, these numbers would be compatible with generation times of 10 or 12.5 (see figure 12 ). It is also reasonable to assume that this strategy is not easy to implement in full, either because some individuals could purportedly try to avoid isolation or due to the fact that many infected subjects have mild symptoms similar to a common flu and neither go to the doctor nor report their state. Therefore, we have simulated a slightly different scenario in which individuals are isolated the same day of their symptoms' onset with a certain efficacy. That is, only a given percentage of the new cases is isolated, while the others are able to roam freely. This framework would also be compatible with having asymptomatic individuals who are able to spread the disease, something that is currently under debate and not yet statistically supported. The equivalence with such hypothetical natural history of the disease in our model is such because we do not apply the prescribed percentage to the total number of infected individuals, but only to those who have just developed symptoms, thus, those that escape will remain infectious as if they were asymptomatic until they recover. In Figure 7B we show the effect that different percentages of new isolated cases would have on the size of the outbreak. Being able to hospitalize all individuals, on average, in less than 1 day enables to effectively stop the disease. Yet, the results also show that even if all infectious are not isolated, as long as more than 60% of the infected individuals are, the effect would be similar and the disease would be effectively eradicated. Lastly, we analyzed the consequences of self-protection measures such as wearing masks, washing more frequently ones hands or avoiding crowded places. To mimic these contexts, we simply reduced the effectivity of the transmission by a certain fraction, and study the final size of the epidemic, see Figure 8A . The results show that a large reduction of at least 60% is needed to contain the disease. Interestingly, if we look at the time to the peak of the epidemic, represented in Figure 8B , we observe that decreasing the transmission not only reduces the size of the outbreak but also delays the peak. Hence, even if this strategy might not be sufficient to completely stop the propagation of the disease in all cases, it could certainly help for preparedness and other clinical responses by delaying the spreading. The exception is when the reduction is very large (in the figure, beyond 60%) as in these cases the peak might occur earlier because the disease dies out.