Scaling analysis of COVID-19 spreading based on Belgian hospitalization data

Bart Smeets; Rodrigo Watte; Herman Ramon

The copyright holder for this preprint . https://doi.org/10.1101/2020.03.29.20046730 doi: medRxiv preprint power law growth phase where H a ∝ t µ . For the latter, we estimate a fractal exponent µ = 2.22. The number of deaths D follows a power law growth D ∝ t µ d with µ d = 3.27. As of March 29th, no significant deviations of neither H a nor D from the power law growth can be observed. Furthermore, Fig. 1 shows the predicted accumulated hospitalization X and infectious population I from a fit using the SIR-X model. The parameters that fit the observed growth of H a are listed in Table 1 . The estimated value of κ 0 , the containment rate of the whole population is very close to zero. Consequently, the public containment leverage P is low as well. The quarantine probability is estimated at a value of Q = 0.780. Furthermore, there is a strong reduction of the reproduction number, with an effective reproduction number of R 0,eff = 1.36, much smaller than the unrestrained reproduction number R 0,free = 6.2. Finally, the SIR-X model predicts that the maximal number of infectious individuals occurs around April 12. Fig. 2(a) shows the number of accumulated hospitalizations as well as deaths due to COVID-19 in comparison to the fitted SIR-x model. Setting an average mortality of 15% for all hospitalized cases [9], we find that the SIR-X model coincides with the number of deaths when including a temporal delay of only ≈ 5 days. Assuming an average hospitalization time of 12 days, and that between 15% and 20% of currently hospitalized patients require intensive care treatment (ICU), we predict based on the SIR-X model the temporal evolution of the current number of patients in ICU - Fig. 2(b-c) . These assumptions align with the observed current number of ICU patients. For the estimated SIR-X model parameters, the number of ICU patients will peak around April 20th. The peak count of ICU patients greatly varies with the average ICU retention time, but will peak at significantly higher values than the current ICU capacity in Belgian hospitals of 2650 beds, Fig. 2(d) . This approximately quadratic growth indicates a small-world network structure with mostly local interactions through which the spreading of the infection occurs. This is consistent with the observation based on data from Belgian telecom operators, which show that more than 80% of Belgians have stayed within their own commune (postal code) for the last two weeks, and that individual displacements of over 40 km have been reduced by 90%. At the time of this writing, no significant deviation from this power law scaling has been observed for the accumulated Belgian hospitalization data. This indicates that the current social network is still sufficiently well connected to continue local spreading of the disease. In part, these local network links could be attributed to the infection of direct family members. Without extensive testing, many infected people will be locked into their homes and pose a contamination risk for their families. In a severe lock-down, this effect should be controlled within a few days. Hence, other factors may contribute to the continuation of the power law scaling. Another spreading mechanisms could be local supermarkets, where in spite of extensive safety measures, significant spreading of the highly infectious corona virus could occur. A solution can be to enforce a more rigid approach, in which supermarkets are viewed as local distribution centres. Most superm