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5. The refined SHARUCD MODEL with import and seasonality (SECOND PHASE):

The current SHARUCD framework evaluates the seasonal effect on COVID-19 dynamics in the Basque Country, after social distancing measures start to be lifted (from May 4 - phase 0 and from May 11 -phase 1 towards the “new normality”). An import factor is also included in the model dynamics, after the full lockdown lifting in July. Although this factor was not important during the exponential growth phase, imported infections play a major role when small numbers are detected (stochastic phase pre/post exponential phase). It refers to infected individuals (most likely asymptomatic) coming from outside the studied population (either an infected foreigner visiting the region or an infected Basque returning to the country and that are not detected by the current testing strategy.)

Note that when the community transmission is under control (social distancing, masks and hygienic measures), the import factor does notcontribute significantly to the epidemic, only starting isolated outbreaks (variable sizes depending on the momentary infection rate), but not driving thecurrent epidemic into a new exponential growth phase.

5.1 Model simulations and short term predictions:

The model shown in section 4 analyses now isolated outbreaks (assuming now import to asymptomatic infection) after lifting of lockdowns and increased detection of asymptomatic due to now intensified contact tracing with time dependent infection rate β, and now also increased import ρ and increased detection of asymptomatic cases ξ over time.

Model parametrization is now also considering the detected positive cases data, in order to disentangle the role of import ρ from community spreading β. From September 15 onwards the daily testing capacity is varying significantly, however the cumulative positivity rates are stabilized (≈ 6.3%). The model predicts an endemic state for positive cases and it is, at the moment, overestimating the mean of positive cases detected using PCR tests. That is because the current assumed detection rate parameter has decreased (and keeps varying) and must be adjusted. More tests would eventually identify those asymptomatic cases predicted by the model, as observed in the last few days with the number of tests increasing significantly. Antigen tests were introduced on Oct. 17, 2020, with an important increase in testing capacity (See Fig. 10b).
As the trend of stationarity continues with import cases (i.e. non detected asymptomatic infections) possibly causing isolated outbreaks, the community transmission is below the threshold, i.e controlled and not increasing to a new exponential phase in the next few days. Note that on October 27, a new lockdown was implemented and transmission rate has decreased even more. Although the trend of stationarity does not appear to be changed, a new control function was included in order to describe the current epidemiological scenario of decreasing detected positive cases.

5.2 Cumulative cases:

Fig. 11: Ensemble of stochastic realizations of the refined SHARUCD-model with import. In a) cumulative positive cases I cum (t), in b) cumulative hospitalized cases C H (t), in c) cumulative ICU admissions C U (t) and in d) cumulative deceased cases D(t).

5.3 Momentary growth rates (λ(t)) and momentary reproduction ratio (r(t)):

Modeling analysis used data referring to notified positive PCR cases, hospitalizations, ICU admission and deceased cases from March 4 up to December 20, 2020 provided by the Basque Health Service (Osakidetza). Hospitalization and ICU admission “by COVID” are notified considering the first positive PCR diagnostic and cases are counted with at most 30 days time-lag between the first positive test and hospital/ICU admission.

Fig. 12: In a) momentary reproduction ratio (r(t)=0.86 for γ=4 on Dec. 20, 2020. In b) the growth rate for PCR positive cases (yellow)

Fig. 13: Growth rates estimations for various variables. In a) hospitalizations(red), b) ICU admission cases (purple). In c) growth rate for recovered (green) and in d) deceased (black).

5.4 Short term predictions of COVID-19 in the Basque Country:

Predictions are made with the refined SHARUCD model parameterized with empirical data described above. Deceased cases are estimated from the current data referring to detected positive cases and severe cases prone to hospitalization and are possibly been overestimated by the model (as PCR method can identify nucleic acid from the virus but can not differentiate between active or residual viral particles). Model predictions are shown as light blue curves. The 95% confidence intervals (CI) are plotted in light purple (shadow). Empirical data are plotted on top of the prediction curve in black.

Fig. 14: 20 days predictions. In a) hospitalizations and in b) ICU admission. In c) deceased cases and in d) detected PCR positive cases.


As the influenza season is expected to start in the Basque Country in the middle of November/beginning of December, careful patients screening would be appropriate, i.e, testing symptomatic patients also for influenza viruses to detect possible co-infections and eventually severe cases caused by other respiratory viruses.