const double population = 47e6;

const int Ndata = ;

double data_time[Ndata]      = {0, 2, 3, 5, 11, 12, 13, 15, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83,84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173};

double data_infected[Ndata]  = {1, 5, 7, 11, 15, 16, 25, 25, 38, 50, 59, 81, 110, 122, 122, 142, 142, 172, 179, 184, 189, 191, 197, 208, 216, 225, 234, 246, 262, 270, 281, 296, 303, 320, 336, 343, 355, 363, 374, 384, 396, 411, 435, 466, 490, 535, 582, 607, 621, 649, 672, 700, 715, 737, 758, 781, 830, 887, 912, 963, 1029, 1109, 1161, 1192, 1214, 1286, 1348, 1471, 1618, 1745, 1888, 1962, 2021, 2093, 2216, 2340, 2474, 2600, 2767, 2862, 2989, 3094, 3215, 3305, 3457, 3594, 3727,3860, 4044, 4257, 4374, 4478, 4738, 4797, 4952, 5206, 5384, 5533, 5811, 6070, 6190, 6366, 6673, 6941, 7188, 7577, 7886, 8067, 8250, 8528, 8975, 9448, 9726, 10105, 10294, 10791, 11252, 11673, 12062, 12750, 13353, 13771, 14168, 14805, 15601, 16268, 16643, 16643, 17975, 18581, 19125, 19913, 20636, 21363, 22053, 22597, 23202, 23873, 24411, 25138};

double data_recovered[Ndata] = {150, 358, 499, 553, 706, 752, 849,873,1048, 1164, 1221, 1253, 1286, 1326, 1353, 1459, 1586, 1607, 1782, 1857, 1905, 1936, 2013, 2039, 2089, 2109, 2148, 2236, 2414, 2593, 2733, 2832, 2946, 3017, 3068, 3983, 5122, 5616, 6757, 7135, 7574, 6774, 6774};

double data_dead[Ndata]      = {0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 3, 4, 4, 4, 4, 6, 6, 7, 7, 7, 8, 9, 9, 10, 11, 11, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 15, 17, 21, 22, 24, 24, 26, 26, 29, 29, 30, 32, 33, 36, 40, 42, 46, 50, 50, 50, 50, 50, 50, 50, 50, 51, 52, 52, 55, 58, 62, 63, 64, 69, 71, 74, 78, 79, 83, 84, 85, 88, 89, 92, 96, 100, 103, 104, 105, 107, 117, 119, 121, 123, 125, 128, 130, 132, 137, 141, 144, 144, 148, 149, 152, 154, 159, 160, 164, 167, 169, 173, 181, 184, 185, 197, 202, 209, 217, 222, 225, 234, 238, 250, 260, 263, 274, 278, 278, 285, 299, 311, 325, 341, 364, 369, 382, 388, 391, 399, 413};

double data_active[Ndata]    = {1, 5, 7, 11, 15, 16, 25, 240, 555, 1523, 1589, 1709, 1811, 1931, 1928, 2028, 1957, 2045, 2136, 2238, 2337, 2429, 2584, 2681, 2771, 3008, 3042, 3395, 3491, 3734, 4033, 4179, 4435, 4680, 4886, 5182, 5489, 5766, 6534, 6710, 7151, 7572, 7975, 7857, 7887, 7917, 7788, 8203, 8791, 10481, 10916};

double ntests[Ndata]         = {21702, 46784, 82946, 85058, 87698, 94507, 97340, 98436, 100683, 102956, 108666, 112169, 115336, 118701, 121956, 124474, 130498, 136361, 140012, 146537, 155314, 158404, 162478, 167417, 169836, 173355, 176059, 180206, 185035, 191394, 196508, 206584, 207987, 214966, 216242, 221234, 225495, 228674, 238920, 241394, 249306, 256060, 263187, 264974, 268171};