Table 1 Left block: parameters fitted from the first wave. Right block: median peak time of the second wave for the 5 typologies (cases a–e) we use in the simulations, with 1 standard deviation. For cases (a–c), the median and error only take into account the 100 simulations, differing by randomly generated matrices \(k_{ij}\). For case (d), we include a variation of \(15\%\) in the \(\gamma _i\)’s for all countries with respect to case (a). For case (e), we include the interval spanned by varying the \(\gamma _i\)’s within \(10\%\) from the fitted values, where the results marked with an asterisk correspond to the tuned countries with a beginning of second wave, as of the 5th of August, 2020.

Austria

\(7.463\pm 0.007\)

\(0.99\pm 0.025\)

\(30.4\pm 0.4\)

\(32.4\pm 0.5\)

\(34.7\pm 0.5\)

\(30.6\pm 0.9\)

\(34.8+0.9-0.7\)

Belgium

\(8.53\pm 0.02\)

\(0.55\pm 0.02\)

\(34.6\pm 0.7\)

\(37.9\pm 0.6\)

\(41.4\pm 0.5\)

\(34.9\pm 1.4\)

\(33.8^*+0.8-0.7\)

Bosnia

\(7.88\pm 0.024\)

\(0.41\pm 0.02\)

\(33.9\pm 0.6\)

\(37.4\pm 0.5\)

\(41.0\pm 0.5\)

\(34.0\pm 1.1\)

\(33.4^*+0.7-0.6\)

Croatia

\(6.268\pm 0.007\)

\(0.71\pm 0.02\)

\(30.9\pm 0.6\)

\(33.5\pm 0.7\)

\(36.6\pm 0.7\)

\(31.1\pm 1.0\)

\(27.7^*+0.1-0.1\)

Czechia

\(9.085\pm 0.014\)

\(0.56\pm 0.03\)

\(33.5\pm 0.7\)

\(36.8\pm 0.6\)

\(40.2\pm 0.5\)

\(33.7\pm 1.2\)

\(32.7^*+0.6-0.5\)

Denmark

\(7.667\pm 0.008\)

\(0.40\pm 0.01\)

\(35.6\pm 0.6\)

\(39.2\pm 0.5\)

\(42.7\pm 0.5\)

\(35.8\pm 1.2\)

\(39.9+1.3-1.1\)

Finland

\(7.190\pm 0.005\)

\(0.385\pm 0.006\)

\(35.4\pm 0.6\)

\(39.0\pm 0.5\)

\(42.5\pm 0.5\)

\(35.7\pm 1.2\)

\(39.8+1.3-1.1\)

France

\(7.711\pm 0.006\)

\(0.58\pm 0.012\)

\(36.0\pm 0.6\)

\(39.3\pm 0.5\)

\(42.6\pm 0.4\)

\(36.3\pm 1.4\)

\(41.1+1.4-1.2\)

Germany

\(7.679\pm 0.007\)

\(0.62\pm 0.02\)

\(35.8\pm 0.6\)

\(39.0\pm 0.5\)

\(42.3\pm 0.5\)

\(36.1\pm 1.5\)

\(39.9+1.4-1.1\)

Greece

\(5.537\pm 0.009\)

\(0.57\pm 0.02\)

\(32.5\pm 0.6\)

\(35.8\pm 0.5\)

\(39.2\pm 0.4\)

\(32.7\pm 1.0\)

\(31.7^*+0.6-0.5\)

Hungary

\(6.022\pm 0.009\)

\(0.47\pm 0.01\)

\(33.9\pm 0.6\)

\(37.4\pm 0.5\)

\(40.9\pm 0.5\)

\(34.2\pm 1.0\)

\(38.1+1.1-0.9\)

Ireland

\(8.580\pm 0.008\)

\(0.60\pm 0.02\)

\(33.1\pm 0.7\)

\(36.1\pm 0.7\)

\(39.5\pm 0.6\)

\(33.4\pm 1.2\)

\(36.6+1.0-0.9\)

Italy

\(8.304\pm 0.004\)

\(0.429\pm 0.008\)

\(39.1\pm 0.6\)

\(42.8\pm 0.4\)

\(46.1\pm 0.5\)

\(39.5\pm 1.7\)

\(43.9+1.7-1.4\)

Netherlands

\(7.904\pm 0.005\)

\(0.525\pm 0.008\)

\(35.2\pm 0.7\)

\(38.6\pm 0.6\)

\(42.1\pm 0.5\)

\(35.5\pm 1.3\)

\(34.3^*+0.9-0.7\)

Norway

\(7.356\pm 0.006\)

\(0.58\pm 0.02\)

\(32.7\pm 0.6\)

\(35.8\pm 0.7\)

\(39.3\pm 0.6\)

\(32.9\pm 1.0\)

\(36.4+1.0-0.8\)

Poland

\(7.13\pm 0.03\)

\(0.182\pm 0.007\)

\(45.7\pm 0.5\)

\(49.3\pm 0.6\)

\(52.6\pm 0.6\)

\(46.2\pm 1.7\)

\(54.6+2.7-2.2\)

Portugal

\(10.323\pm 0.014\)

\(0.517\pm 0.022\)

\(34.7\pm 0.7\)

\(38.1\pm 0.6\)

\(41.6\pm 0.5\)

\(35.0\pm 1.4\)

\(38.7+1.2-1.0\)

Serbia

\(9.323\pm 0.012\)

\(0.628\pm 0.017\)

\(32.6\pm 0.6\)

\(35.6\pm 0.6\)

\(38.9\pm 0.5\)

\(34.0\pm 1.1\)

\(29.2^*+0.3-0.3\)

Slovakia

\(5.67\pm 0.02\)

\(0.59\pm 0.04\)

\(31.7\pm 0.7\)

\(34.8\pm 0.7\)

\(38.2\pm 0.6\)

\(31.9\pm 1.0\)

\(30.7^*+0.5-0.4\)

Slovenia

\(7.299\pm 0.007\)

\(0.656\pm 0.017\)

\(30.7\pm 0.6\)

\(33.5\pm 0.7\)

\(36.7\pm 0.6\)

\(30.9\pm 0.9\)

\(29.7^*+0.3-0.3\)

Spain

\(8.747\pm 0.008\)

\(0.46\pm 0.01\)

\(38.2\pm 0.7\)

\(41.8\pm 0.5\)

\(45.2\pm 0.5\)

\(38.5\pm 1.8\)

\(33.8^*+0.8-0.7\)

Sweden

\(11.56\pm 0.04\)

\(0.162\pm 0.008\)

\(47.8\pm 0.5\)

\(51.3\pm 0.5\)

\(54.6\pm 0.6\)

\(48.3\pm 2.2\)

\(55.8+2.9-2.4\)

Switzerland

\(8.196\pm 0.003\)

\(0.72\pm 0.01\)

\(32.4\pm 0.6\)

\(35.1\pm 0.7\)

\(38.1\pm 0.7\)

\(32.6\pm 1.2\)

\(35.8+1.0-0.8\)

UK

\(8.353\pm 0.007\)

\(0.368\pm 0.007\)

\(41.0\pm 0.6\)

\(44.6\pm 0.4\)

\(48.0\pm 0.5\)

\(41.3\pm 1.9\)

\(46.2+2.0-1.6\)