Modelling COVID 19 in the Basque Country from introduction to control measure response

Abstract

In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system's necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. The growth rate [Formula: see text] was calculated from the model and from the data and the implications for the reproduction ratio r are shown. The analysis of the growth rates from the data led to improved model versions describing after the exponential phase also the new information obtained during the phase of response to the control measures. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of "social distancing" and home quarantining.

Figure 1

Cumulative COVID-19 cases of tested positive ($I_{\mathit{cum}}$), hospitalized cases ($C_H$), ICU admission ($C_U$), recovered ($C_R$) and deceased cases (D). The imposed control measures and its gradual lifting process are marked with arrows with the effective dates of implementation.

Figure 2

Ensemble of stochastic realizations of the SHARUCD-type model.The mean field solution is shown in light blue. Empirical data are plotted as black/red dots. (a) Cumulative tested positive cases $I_{\mathit{cum}}(t)$ (yellow lines), (b) cumulative hospitalized cases $C_H(t)$ (red lines), (c) cumulative ICU admission $C_U(t)$ (purple lines), (d) cumulative deceased cases D(t) (black lines), and (e) cumulative recorded recovered $C_R(t)$ (green lines). (f) Semi-logarithmic plot of the data and the mean field curves of all variables. For quite some time all mean field curves and the data are in parallel, and we could calculate the slope from the model parameters as growth rate $\lambda$, see light blue line.

Figure 3

Numerical likelihood functions for the parameters (a) recovery rate $\gamma$, (b) infection rate $\beta$, (c) diseased induced mortality rate $\mu$ and (d) rate of ICU facilities admission $\nu$, and (e) hospital admission ratio $\eta$, (f) infectivity of mild/asymptomatic relative to the hospitalized $\varphi$ and (g) recording rate of mild/asymptomatic cases $\xi$. Parameter values are presented in Table 1 (supplementary material).

Figure 4

Ensemble of stochastic realizations of the SHARUCD-model with control and data matching, starting from March 4, 2020. The mean field solution without control is shown in light blue. Empirical data from March 4 to April 13, 2020 are plotted as black/red dots. Empirical data from April 14 to April 21, 2020 are plotted a green squares. For short-term predictions. (a) Cumulative tested positive cases $I_{\mathit{cum}}(t)$ (yellow lines), (b) cumulative hospitalized cases $C_U(t)$ (red lines), (c) cumulative ICU admission $C_U(t)$ (purple lines), (d) cumulative deceases cases D(t) (black lines), and (e) cumulative recovered $C_R(t)$ (green lines).

Figure 5

Ensemble of stochastic realizations of the SHARUCD-model. The mean field solution without control is shown in light blue. Empirical data, from March 4 to April 20, 2020 are plotted as black/red dots. Empirical data, from April 21 to May 9, 2020 are plotted as green dots. For long term predictions, (a) cumulative hospitalized cases $C_H(t)$ (red lines, up to July 12, 2020) and (b) cumulative deceases cases D(t) (black lines, up to August 1, 2020). The scale used here is 1:2 for hospitalizations and deceased cases.

Figure 6

(a) Growth rate estimation from the data on positive tested infected cases, and (b) reproduction ratio from the same data. With $\mathrm{\Delta }t=5$ days and $\tau =7$ days, the sigmoidal black curve represents the values of ${\lambda }_1$ and $r_1$ computed on the basis of $\beta (t)$.

Figure 7

Growth rate estimation for various variables. (a) Growth rate for tested positive cases (yellow), hospitalizations (red) and ICU (purple). (b) Growth rate for recovered (green) and deceased (black). Two groups of growth behaviour in response to the lockdown measures are observed,’crossing the threshold of zero growth at different times.

Figure 8

Ensemble of stochastic realizations of the refined SHARUCD-model and data matching. The mean field solution without control is shown in light blue. Empirical data are plotted as black/red dots. (a) Cumulative tested positive cases $I_{\mathit{cum}}(t)$, (b) cumulative hospitalized cases $C_U(t)$, (c) cumulative ICU admissions $C_U(t)$, (d) cumulative deceases cases D(t) , (e, f) cumulative recovered $C_R(t)$.

Figure 9

Adjusted SHARUCD model to synchronize ICU admissions with tested positive cases and hospitalizations. (a) Data and mean field solutions in natural scale. (b) Data and mean field solutions in semi-log scale with adjusted mean field curves and growth rate $\lambda$ as light blue line.

Figure 10

(a) Cumulative hospitalized cases $C_H(t)$ (red lines), (b) cumulative ICU admissions $C_U(t)$ (purple lines), (c) cumulative deceased cases D(t) (black lines). Empirical data are plotted, up to May 4, 2020, as black/red dots.