Aleksandar Maričić, decembar 2021. – Konarevo, Srbija
Ovaj program analizira vremenske serije podataka o sunčevoj aktivnosti (broju sunčevih pega) i epidemiološkim podacima COVID-19 (aktivni slučajevi, novi slučajevi, letalitet) od marta 2020. do decembra 2021. godine. Program učitava i normalizuje podatke o broju aktivnih slučajeva globalno i u Srbiji, dnevnim novim slučajevima i letaliteta, kao i broj sunčevih pega za svaki dan.
Kroz višestruke vremenske nizove, program koristi biblioteke za crtanje grafikona (matplotlib) kako bi vizualno prikazao korelacije između solarne aktivnosti i epidemioloških trendova. Na grafikonu su jasno označeni vremenski intervali i meseci radi lakše interpretacije.
Cilj programa je da istraži potencijalnu povezanost između fluktuacija sunčeve aktivnosti i dinamike širenja COVID-19, oslanjajući se na hipotezu o “Zemnom odjeku” sunčevih oluja, kako je prvi predstavio Aleksandar Čiževski. Vizuelni prikaz omogućava prepoznavanje obrazaca i sinhronizacija u promenama broja sunčevih pega i epidemioloških indikatora, što može poslužiti kao osnova za dalju statističku i regresionu analizu.
Uvod i teorijska osnova
Program koji je ovde predstavljen inspirisan je istraživanjima Aleksandra L. Čiževskog, pionira u oblasti heliobiologije, koji je u svom kapitalnom delu:
Чижевский А. Л. (1976). Земное эхо солнечных бурь (Zemni odjek Sunčevih oluja). М., «Мысль».
izložio hipotezu da varijacije u solarnoj aktivnosti – naročito Sunčeve oluje i geomagnetne promene – mogu imati značajne efekte na biološke sisteme, uključujući i kolektivno ponašanje ljudi, učestalost bolesti i psihološke poremećaje.
Cilj i hipoteza
Autor programa je postavio sledeću radnu hipotezu:
„Postoji vidljiva veza između promena u solarnoj aktivnosti i oscilacija u broju obolelih od COVID-19 na globalnom i lokalnom nivou.“
Ova hipoteza se uklapa u okvir heliobioloških istraživanja i predstavlja nastavak Čiževskog u savremenim uslovima pandemije.
Podaci i metode
Korišćeni su dnevni podaci za period od 15. marta 2020. do 1. decembra 2021.:
- Broj Sunčevih pega (
sunce[]) – preuzet sa SILSO baze (WDC-SILSO, Royal Observatory of Belgium). - Broj aktivnih slučajeva COVID-19 (
aktivni[]– svet,aktivniS[]– Srbija). - Broj umrlih (
letal[]) – za analizu letaliteta.
Podaci su vizualizovani uz pomoć biblioteke Matplotlib, normalizovani radi zajedničkog prikaza na jednoj skali.
Rezultati i interpretacija
Grafikon pokazuje višemesečne oscilacije u broju Sunčevih pega i broju aktivnih slučajeva virusa. Vizuelno, uočava se:
- Povećanje broja pega tokom kasne 2021. godine (oktobar-novembar),
- Paralelni porast aktivnih slučajeva virusa u istom periodu,
- U nekim slučajevima, porast solarne aktivnosti prethodi epidemijskom talasu za 10–20 dana (što može ukazivati na vremenski pomak biološke reakcije).
Ovo se može tumačiti kao „zemni odjek“ solarne aktivnosti, kako je to Čiževski nazivao – indirektni odgovor biosfere na elektromagnetne i geomagnetne promene izazvane aktivnošću Sunca.
# Izvor za aktivnost sunca:https://www.sidc.be/SILSO/datafiles
# Source: WDC-SILSO, Royal Observatory of Belgium, Brussels
# https://www.sidc.be/SILSO/datafiless
# Izvor za statistiku virusa Covid 19
# https://www.worldometers.info/coronavirus/country/serbia/
# Izvor za suncano vreme
# NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION
# https://www.swpc.noaa.gov/communities/space-weather-enthusiasts
# Program napisao Aleksandar Maričić, 3. decembar 2021. Konarevo, Srbija
# e-mail: sale.maricic@gmail.com
dani = []
virusx = []
brzr=[]
dnevno=[]
letalitet=[]
aktivniSx=[]
#aktivni slucajevi u srbiji
aktivniS= [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,5,18,24,35,46,47,56,71,88,102,132,168,218,243,285,365,435,478,607,686,727,835,
990,1098,1383,1526,1803,2024,2268,2483,2683,2916,3188,3150,3569,3971,4374,4772,5046,5240,5443,5635,5783,5955,6074,6245,6476,
6704,6904,7069,7259,7487,7641,7747,7720,7786,7754,7617,7482,7281,7087,6893,6668,6423,6249,6066,5912,5789,5667,5669,5595,5531,
5312,5246,5155,5064,5034,4921,4758,4621,4588,4533,4471,4460,4443,4426,4415,4489,437,226,298,367,432,502,575,650,545,601,659,754,
847,939,1032,686,731,775,861,954,1068,1187,1312,1433,1625,1783,1996,2142,2459,2756,2737,2942,3084,3339,3707,3911,4091,4294,
4574,4858,4662,4716,4776,4735,4762,4722,4619,4649,4575,4544,4568,4571,4531,4501,4353,4305,4256,4196,3554,3430,3315,3224,3154,
3096,2999,2873,2817,2454,2220,2128,2361,1947,1897,1612,1662,1612,1411,1361,1222,985,983,924,859,696,747,723,665,714,677,664,
664,597,544,524,530,570,464,398,469,575,419,463,466,546,607,689,756,659,720,800,882,956,1030,1084,1006,1042,1040,1049,1040,
1085,1061,1044,1134,1194,1264,1354,1447,1475,1470,1592,1772,1944,2185,2395,2498,2547,2766,3219,3584,4043,4679,5142,5310,6195,
7421,8738,10131,11703,12949,13486,15137,17335,19394,21350,23515,25211,25950,28016,30938,33938,36384,38878,40976,42244,45421,
49585,54892,59268,62630,65444,68229,72394,77861,84149,89106,92611,95449,98174,102351,106788,111777,114565,115855,115555,115858,
117902,120711,123037,122729,120829,118218,115370,114213,113387,112292,109203,105172,100904,96807,93984,92601,90135,86140,81536,
76836,72861,70318,68559,66559,62749,59303,56140,53945,52710,52058,50160,48298,45641,43345,41615,40557,40131,39453,38068,36225,
34610,34114,33895,33575,32508,31564,30165,29696,29001,29312,29356,28855,28430,27706,27191,27179,27689,28304,28589,28869,28907,
28788,29039,29570,30340,30817,30665,30448,30242,29856,30123,31224,32046,32775,33285,33940,34928,36501,38432,40060,41385,42507,
43316,44857,47392,50062,52597,54858,55910,56391,57850,59984,62056,63695,65106,65738,66376,70982,72841,75076,77615,79452,79980,
80153,81058,82458,84235,86420,87551,87474,91324,86686,89824,92599,93318,93916,93132,91521,89778,88829,87137,86076,85251,83538,
80801,78466,76815,74741,73218,72171,70247,66842,64341,62499,60532,59120,58201,56565,53863,52236,50757,49493,48443,47324,45734,
43152,41247,39579,38137,36921,36130,34582,32452,30507,28913,27576,26408,25501,24218,22642,21081,19761,18756,17933,17336,16490,
15455,14429,13475,12588,11856,11353,10710,9763,8964,8297,7795,7308,6949,6520,5951,5505,5170,4975,5178,4689,4431,4158,4274,3699,
3531,3391,3375,3214,3047,2849,2700,2596,2528,2489,2393,2245,2125,1992,1924,
#juli
1890,1822,1777,1723,1541,1487,1590,1686,1647,1636,
1634,1650,1713,1764,1919,1998,2078,2129,2254,2359,
2513,2663,2788,2925,3018,3156,3347,3572,3785,4069,4249,
#avgust
4405,4666,4933,5217,5629,6070,6426,6692,7216,7781,
8697,9236,10104,10869,11397,12350,13546,14687,16046,17333,
18453,19274,20628,22261,24025,25895,27871,29432,30362,31773,33769,
#septembar
36042,38561,41365,43572,44886,47494,50903,54943,59265,64110,
67732,70518,74441,79711,84899,90188,96035,100444,102716,105793,
109501,113078,116059,119722,121809,122128,123228,125865,127947,130033,
#oktobar
132302,132460,130073,128427,128014,127593,127825,128973,128203,125772,
124274,124722,124961,125552,126591,125900,122513,120804,120914,121387,
122301,124665,125427,123969,122726,123587,124133,125174,126586,126888,125752,
#novembar
131585,138636,118663,119709,118969,116112,112251,109274,106686,104545,
102811,106566,96370,92200,88991,92709,84147,82438,79630,75169,
70516,67164,64474,62305,61096,59084,56190,53260,51444,49889
#decembar
]
#Active Cases
aktivni= [970,1198,1650,2325,3086,4835,6244,7948,9873,11892,14388,17011,20061,23657,27046,29768,32614,34604,36871,38612,39812,52662,56893,58053,58702,59319,59513,59416,58029,56775,55349,54532,52661,51097,49310,47655,45341,44184,43434,43202,42759,43142,43644,45777,48716,51784,55296,60528,66460,75716,87666,101643,115283,131878,149431,169472,193637,221858,255433,283819,315803,354185,390945,432175,481101,534599,588666,636211,681097,738386,793514,844828,903278,956501,1003518,1054262,1098730,1145223,1195889,1259454,1303767,1345539,1387222,1415376,1452098,1485462,1531846,1570911,1601865,1648548,1678109,1716163,1755661,1770913,1807374,1845645,1857650,1886741,1920030,1956453,1997581,2027290,2066649,2100692,2126460,2154228,2196743,2237308,2253969,2275533,2300280,2315046,2330845,2371527,2403384,2433677,2463535,2490843,2520295,2547864,2581210,2559279,2586596,2609953,2621148,2631687,2656842,2673474,2717072,2745317,2729769,2759536,2755737,2707777,2741833,2781064,2819972,2874232,2893968,2939051,2929229,2948480,2991670,3005312,3040257,3062382,3086919,3106799,3139570,3194953,3225775,3242846,3288626,3321958,3351757,3435203,3486451,3556380,3619089,3662900,3706561,3769221,3773175,3846902,3898365,3977063,4034584,4031552,4065024,4127873,4210682,4275018,4359574,4430860,4499162,4537001,4534650,4592166,4661093,4752705,4775817,4806428,4834412,4914195,5007689,5068260,5147442,5173291,5187465,5233042,5268811,5326373,5406051,5469966,5455312,5470019,5488962,5569470,5655397,5739641,5718145,5710013,5712398,5724682,5783813,5840513,5906795,5886197,5852315,5846406,5854453,5899435,5960521,6014422,6041648,5973626,5969266,5963055,6007043,6079440,6120316,6135081,6139027,6134165,6156594,6210699,6238946,6295774,6311442,6276672,6267790,6267611,6309627,6368576,6412511,6429386,6410541,6414882,6435477,6489680,6493652,6529927,6518051,6458415,6435474,6441303,6482181,6533281,6574398,6582944,6554784,6556674,6562418,6615709,6690359,6735099,6739125,6735345,6747105,6804936,6888925,6967624,7093970,7121889,7115621,7155010,7219030,7331414,7432570,7563931,7651336,7716551,7805530,7924139,8101773,8311069,8509291,8669515,8752333,8908475,9100420,9340190,9597747,9818924,9979497,10111845,10261755,10456951,10719867,10995429,11275765,11488970,11622707,11805151,12059203,12097361,12349936,12533318,12700629,12766394,12785132,12913091,13087969,13280886,13408461,13502108,13538507,13598830,13574552,13692467,13729008,13800216,13841900,13778868,13782803,13806976,13924469,14059191,14132025,14228763,14207001,14232198,14267910,14383806,14478352,14576481,14683463,14670582,14704341,14784205,14950318,15155326,15226012,15359350,15321897,15353635,15449781,15585023,15686928,15643989,15626741,15530905,15556056,15673838,15894282,16112378,16143981,16246608,16124541,16285182,16489839,16786864,17142460,17369167,17583856,17618351,17709663,17904294,18051020,18216598,18363423,18454632,18402513,18263096,18275931,18367221,18488615,18577450,18619842,18435525,18338852,18366141,18338598,18374207,18376094,18365924,18077103,17926104,17800819,17733856,17701044,17591304,17489597,17257193,17062578,16867256,16771901,16674035,16578826,16446487,16229666,16034669,15902740,15791153,15715449,15621888,15532321,15332585,15186511,15119273,15082751,15057025,14976731,14904579,14750399,14645535,14656801,14616794,14614324,14572361,14568917,14403324,14335344,14363665,14391068,14449748,14498509,14510923,14429668,14410727,14481252,14519425,14627875,14730356,14791007,14692201,14639221,14678743,14786384,14950130,15094304,15191773,15146801,15159968,15269960,15440435,15619293,15698377,15769442,15715938,15734355,15832994,16005721,16217432,16376454,16472496,16458179,16543805,16709455,16900315,17085015,17251677,17307768,17264832,17327568,17435462,17586326,17748780,17841683,17910238,17771554,17774769,17835250,17922227,17960591,17918121,17885748,17734096,17606583,17614255,17629735,17680331,17598013,17521216,17312331,17191421,17092209,17017616,16913927,16718074,16530353,16234928,15983994,15846250,15711746,15589897,15418316,15286477,14985183,14775751,14618911,14488092,14351687,14185703,14032404,13795090,13541103,13373570,13273349,13186428,13034769,12867075,12599050,12405386,12283053,12213865,12172463,12007228,11926500,11763839,11663048,11594641,11579044,11552910,11520419,11467194,11337205,11284637,11308516,11377614,11438818,11439120,11439033,11382991,11339799,11356605,11416559,11485828,11532587,11564424,11516202,11518751,11597248,11703738,11823819,11906067,11930367,11915786,12008068,12181865,12383580,12586814,12755670,12883844,12916679,13048350,13196798,13362822,13512030,13696765,13855114,13885610,14016656,14223446,14463317,14699410,14887024,15039923,15096578,15236003,15462088,15685228,15904298,16062619,16173353,16152520,16194062,16294147,16426295,16639082,16758533,16832253,16797065,16869978,17007821,17205935,17409917,17536921,17632329,17584317,17644645,17804944,17974838,18165948,18282737,18367158,18319522,18355841,18403887,18534851,18681800,18727018,18759376,18667573,18601900,18584058,18493386,18518118,18554068,18556867,18390032,18297975,18285333,18343679,18409677,18409287,18373074,18226371,18168150,18143319,18161380,18234964,18224028,18198455,18068979,17953864,17919505,17931995,17937631,17895000,17821643,17604403,17515860,17466831,17487844,17479116,17493411,17471920,17378245,17279243,17288559,17338257,17375501,17411941,17421480,17325955,17282503,17334617,17412513,17460143,17509207,17539416,17435219,17457139,17500254,17604518,17691366,17769908,17821242,17765795,17769065,17803803,17917085,18041046,18139124,18191603,18131086,18146757,18253585,18415428,18515330,18604553,18664845,18663599,18713078,18816260,18994434,19142890,19256711,19339780,19375181,19479927,19625367,19801102,19961406,20068615,20158138,20154273,20262105,20473352,20716975
]
#Daily New Cases
novi= [ 0,271,475,701,787,1784,1479,1764,2016,2137,2626,2857,3253,3927,3728,3184,3453,2685,3004,2569,2057,14180,5174,2682,2132,2158,2031,
1880,534,1034,1058,1038,628,993,861,1136,1459,1818,2204,2633,2613,3304,3165,4318,5049,5739,5846,7208,8772,11274,14375,16659,
17388,18828,20398,23894,28017,32093,38443,33976,37002,43723,46280,49842,62399,67213,67779,61190,64194,76150,78257,79299,86756,
82180,74285,75876,83711,89070,89821,98041,85764,76721,76413,80436,87526,87878,90887,85362,78952,83551,82335,84635,88708,97192,
91697,75773,71555,79208,88919,89018,95833,83454,82611,81591,84120,97217,97135,97297,88991,80837,73811,89544,92625,98635,102956,
97515,84337,92207,99219,106270,109469,110005,103039,98727,92237,95770,110094,120262,129491,126924,111485,103732,120308,123952,
134316,133883,131626,117295,110283,124932,140057,141964,145070,138014,126872,128676,148797,151080,146094,186061,162746,134578,
143513,169230,179814,186426,199399,184428,168349,163724,183517,203893,216184,219183,201083,180733,176383,216285,220750,231078,
242961,222981,202034,196468,228147,241917,253913,245375,232751,223776,205128,246407,285833,280269,294173,268444,224832,218432,
255716,295752,292129,295847,265168,224552,202280,260611,278348,287922,287574,277217,227151,220013,274447,294745,291053,294881,
270485,221760,205224,265196,280622,276760,268924,272740,217425,219774,262589,281769,282032,294910,269203,230619,250890,268201,
292601,294225,311490,282708,244357,206785,252239,295262,307175,322363,296175,258503,250632,289681,312068,318811,328653,304359,
259701,239506,287471,317960,319629,328970,306967,262928,238878,295278,322302,326924,333038,305021,261140,272417,316425,352800,
360979,365346,378799,295305,275838,324630,387724,404393,419920,402998,349454,338321,396229,447454,485743,495541,485560,435537,
400954,472381,518212,549976,575070,513186,472954,454347,504326,574860,625363,629281,640307,507881,472096,571802,626796,654267,
661424,614268,521646,492160,577526,622543,665064,669388,618514,527404,528768,573774,643213,626543,610496,600876,528147,491282,
592630,646356,693061,694940,654953,553718,518730,613601,660833,702769,713235,666320,553963,526988,610223,726902,738084,721570,
647672,564763,535794,623750,698426,698329,543326,472193,449396,495063,642932,738268,762421,649672,569293,544878,557670,719985,
807275,843545,844898,773450,645450,588370,687420,745635,752369,762968,680151,560558,477222,595085,663842,652312,640234,604667,
484624,437251,534434,589635,599894,584225,531774,418152,390109,456799,485896,507390,496926,443125,363397,319842,389735,441946,
444068,428673,387688,305055,262514,346460,397316,402393,412471,388327,318279,285206,378757,444476,449080,436634,398230,322118,
294621,372220,445991,450484,454005,414685,379675,292509,394273,468872,482114,494290,454141,378036,336539,456070,535036,552431,
558259,519355,437684,423754,505529,590719,635047,634409,595760,503499,456782,549425,646455,706818,652554,568382,552928,480853,
632412,690002,746649,791909,723634,654460,584249,743399,813246,843245,837432,806207,731013,656552,830438,887727,889544,901831,
846750,746650,671814,837361,892376,904019,876155,818457,698126,670010,785675,849818,860246,841621,798261,667044,608270,717345,
756456,747868,700843,648839,550306,535468,618071,664346,657090,625307,584828,491074,445076,525390,562678,538379,510597,502832,
415386,367697,450417,492556,476999,421839,411709,340060,314194,365250,423996,438400,416647,382577,310599,302929,373620,401756,
390942,405718,368933,305291,280787,378313,434421,406864,413618,382477,323550,318371,384510,398613,434322,441876,399218,355040,
347971,435087,464579,489155,497078,450061,402762,399693,515841,557405,568097,567520,527506,495069,433338,521229,566413,573085,
584084,547288,495771,463827,606634,665746,677105,654360,598016,548356,500144,625418,694824,716583,708209,643466,570749,522696,
659288,708573,723819,734453,649807,565633,531676,673022,710262,746531,723609,639886,565388,526593,680542,737882,736713,728053,
642787,561297,536450,640042,687170,694941,679936,585025,541229,499275,540986,613986,628787,609981,553517,488574,448934,525515,
574921,586651,576582,495293,428522,412017,486196,533739,525027,513626,442844,398583,382667,439113,492957,501552,481363,410557,
358295,347984,422971,458848,470740,454075,396523,353325,332467,403434,446998,453966,441840,391908,347717,353049,423089,458848,
472178,462835,418013,361827,341166,440580,480623,489868,475655,429179,371904,363176,407193,489067,526668,512101,464432,393084,
388611,479162,553103,564281,538638,490566,416480,429661,517476,600370,623858,603772,556439,461154,470739,587836,640658,636805,
619317,542458,462875,477012,611412,682526,694461
]
letal= [142,106,98,136,117,121,113,100,158,81,64,37,58,65,54,73,
67,85,83,103,107,106,228,198,274,331,361,455,418,706,653,839,1002,1125,1417,1668,1717,1986,2609,2633,3154,3571,3858,3555,4329,
4806,5443,6439,6291,6428,5407,5826,7901,7063,8010,7408,6586,5952,6014,7662,8473,7266,8819,7009,5352,6101,7709,7013,7188,6773,
6700,4543,5228,7445,7457,6375,6612,6314,4519,5343,6662,7364,6419,6202,5463,5147,4630,6482,5905,5971,5815,5008,4070,4502,5950,
5412,5805,5549,4846,4130,4454,4708,5737,5333,5468,4832,4134,4115,5609,5650,5655,5326,4923,4405,4218,5637,5872,5563,5432,5125,
4328,4554,7430,5902,5903,5823,5051,4426,4051,5871,5504,5597,5376,5107,4240,4720,5756,5542,5664,5684,5206,4292,4569,6216,5937,
6075,5956,5662,5047,4831,6343,6361,6631,6316,5773,5135,5048,6734,7576,6863,6868,6315,5090,5310,6489,7229,6935,6767,6182,5011,
5391,6861,7363,7031,6961,6022,5376,5314,6727,6962,7003,6448,6031,5135,5190,6877,6954,6630,6599,6084,5031,5025,6650,6599,6457,
6232,5688,4695,4879,6394,6509,6160,6078,5291,4596,4511,5004,6115,5913,5907,5240,4338,4770,6288,5971,5662,5799,5165,4311,4193,
5744,5816,5431,5504,5271,4082,3928,5764,5686,5616,5689,4969,4321,4697,5829,6002,6505,5914,5337,4659,4216,5257,6208,6142,6365,
5829,4313,4931,6503,6915,6568,6659,6009,4853,5616,7376,7249,7233,7656,6960,5912,6375,8633,9529,9088,9491,8094,6722,7437,9711,
10338,9943,10125,9712,7546,8139,10964,11966,11368,11374,9623,8354,8885,12311,12401,11407,11225,10027,8214,9290,12556,12616,
12786,12507,10814,8479,9185,12439,12581,12973,12658,11322,8590,9740,13437,13965,13498,13106,11499,8993,10508,13763,13731,12271,
9505,8089,8614,10395,14807,15558,14130,10567,9067,8499,10515,14739,15024,15105,15361,13165,9867,10617,16619,16893,16011,15528,
14016,10043,10558,16050,17474,16992,15987,14743,10398,11059,17024,17520,16856,15264,13170,9731,10843,15533,15411,14326,14242,
11652,8228,9482,13661,13796,13174,12188,10558,7314,7368,10393,11189,11341,11189,8871,6924,7172,10823,10665,10572,9855,8462,6579,
7207,9947,10734,10137,9757,8107,6112,7094,9168,10038,9815,9556,8376,6181,7278,10291,10466,10160,10530,8619,6320,7629,10885,10419,
10764,11629,10128,7236,8081,11353,12217,11824,10651,9189,7626,8097,12467,13257,14025,13557,11442,8999,9574,13278,13838,14266,
12969,12134,10096,10644,14712,14315,13845,14715,14139,10540,11518,15651,15671,15854,14676,13957,10877,11627,14770,15287,14623,
14535,13647,11045,11650,14597,14645,14532,14166,13397,10727,11597,14891,13749,14088,13650,11749,10633,9630,12897,12805,11976,
12100,11058,8645,9056,11170,11377,11131,10567,9452,7840,7981,10355,10274,10232,9499,8711,6968,6843,9294,9518,8802,9116,8806,6890,
6511,8980,9141,8714,8791,7731,6415,6408,7950,8833,8365,8589,7396,6364,6374,8290,8501,8925,8527,7675,6643,6566,8212,8720,8615,8767,
7391,7115,6991,8542,8712,9023,8782,8523,7189,7646,9618,10278,10565,9512,9256,8086,8366,10341,10195,10603,10347,9714,8576,8408,
11036,10723,11015,10511,9402,8894,8304,10574,11074,11509,10789,9667,9170,8154,11073,11856,11350,10563,9762,8388,8303,9750,10980,
11317,10425,8948,7632,7540,9095,10251,10309,9620,8954,7153,7395,9489,10768,9862,8976,7908,6812,6315,8800,9731,9199,8909,7074,
6028,5955,8660,9236,8315,7701,6749,5549,5429,7877,8578,8115,7915,6434,5062,5207,7122,7891,7864,7302,6248,4989,5338,7462,7664,
7651,8012,6538,5357,5611,7857,9021,8267,7896,6670,5164,5686,7336,8025,7763,7896,6972,5178,5900,8012,8570,7594,7876,6725,5162,
5728,7786,8611,8392,7941,6598,4873,6026,8467,8422,7658,7213,6428,5006,5856,8122]
sunce=[ #259
#15 februar 2020
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
#mart 2020 -31
0,0,0,0,0,0,2,16,11,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,3,11,
#april 2020-30
13,13,13,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,13,26,15,24,20,
#maj - 31
4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
#juni -30
6,0,9,11,13,16,16,16,14,12,11,11,11,11,8,0,0,0,0,0,0,0,0,0,0,6,4,0,0,0,
#juli -31
4,2,0,7,5,5,8,0,0,0,0,0,0,0,2,0,0,0,0,0,6,11,11,11,11,11,11,20,21,21,21,
#avgust -31
26,15,11,11,12,14,17,12,13,13,12,17,10,5,0,0,0,13,16,12,3,0,0,0,0,0,0,0,0,0,0,
#septembar-30
0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,7,5,4,0,0,0,0,0,
#oktobar -31
0,0,0,0,0,0,0,6,20,18,20,14,0,4,13,13,14,21,17,14,14,12,17,18,19,22,41,35,42,34,26,
#novembar -30
5,9,16,26,31,41,38,44,29,29,29,32,26,20,5,0,10,13,13,13,26,34,48,44,53,58,75,86,96,87,
#decembar -31
56,48,45,41,37,25,21,14,14,12,12,11,11,13,20,14,13,7,0,0,12,12,24,28,31,35,33,30,32,32,34,
#2021
#januar - 31
24,17,0,0,0,0,0,0,0,0,0,0,0,3,14,12,14,12,20,21,25,35,32,23,27,17,20,7,0,0,0,
#februar 28
0,9,7,0,0,0,0,2,2,0,0,0,0,0,0,0,0,10,9,9,10,16,36,38,34,18,17,13,
#mart 31
10,16,35,30,13,7,21,14,15,17,22,14,11,23,24,19,13,13,13,11,8,22,27,30,27,25,19,12,12,9,0,
#april 30
0,0,4,12,11,6,0,0,0,0,10,14,19,21,25,35,15,18,36,57,46,44,37,54,55,50,55,46,37,28,
#maj 31
10,0,0,0,0,0,10,17,20,34,32,33,30,26,28,13,14,28,27,20,14,19,27,31,41,41,41,31,15,26,30,
#juni 30
22,29,31,35,38,38,49,34,25,27,19,8,15,12,11,11,12,21,15,14,13,16,12,11,23,19,33,46,56,54,
#juli 31
57,61,61,51,44,50,20,17,12,16,22,23,19,29,22,35,50,48,49,46,72,75,55,31,36,31,21,7,4,0,2,
#avgust 31
8,13,17,17,24,9,0,0,7,0,19,8,10,20,13,20,15,13,22,13,17,19,17,21,35,48,70,75,51,43,40,
#septembar 30
38,33,25,70,75,83,74,98,102,97,74,50,34,23,10,0,0,0,13,44,65,81,69,61,46,50,49,56,70,45,
#oktobar 31
36,34,26,35,31,26,16,19,24,39,30,18,20,21,12,11,0,18,13,12,18,37,50,41,68,92,104,100,85,78,68,
#novembar
51,43,33,26,35,34,28,39,45,39,41,35,27,20,23,32,28,22,22,21,21,23,32,34,26,40,38,45,41,54
]
#virus = [3.2558,3.46688,3.590395,3.681358,3.695,3.52435,3.4429,3.8371,4.0031,4.084455,3.7956,4.2632,
# 4.219,4.104789,4.0031,4.838589,4.77498,5.23889,5.29,5.30,4.72,5.40,5.88,6.36,5.964886,6.68277,6.24920850294]
import matplotlib.pyplot as plt
for t in range(0, 655):
dani.append(t+1)
brzr.append(aktivni[t]/130000)
dnevno.append(novi[t]/8000)
letalitet.append(letal[t]/300)
aktivniSx.append(aktivniS[t]/1000)
# virusx.append(100/virus[t])
plt.figure(figsize=(21.5,6))
plt.xlim(1,686)
plt.ylim(0,150)
plt.plot(dani,sunce, 'r', label='Broj pega na Suncu')
#plt.plot(dani,virusx, 'b')
#plt.plot(dani,sunce8, 'm')
#plt.plot(dani,sunce7, 'y')
#plt.plot(dani,sunce6, 'g')
#plt.plot(dani,mrtvi, 'k')
plt.plot(dani,brzr, 'g', label='Aktivni slucajevi u Svetu')
#plt.plot(dani,dnevno, 'b', label='Novozaraženi u Svetu')
#plt.plot(dani,letalitet, 'k', label='Letalitet u Svetu')
plt.plot(dani,aktivniSx, 'm', label='Aktivni slucajevi u Srbiji')
plt.legend(loc='best', shadow=True)
plt.title("Korelacija aktivosti Sunca i virusa Covid 19 u Svetu i Srbiji")
plt.ylabel("Sunce,Letaliet, bolesni/1000, zarazeni/100, ")
plt.xlabel(" Broj dana od 15.marta 2020 do 1.decembra 2021")
# x coordinates for the lines
xcoords = [ 15,46,76,107,137,168,199,229,260,290,321,
352,380,411,441,472,502,533,564,594,625,655]
# colors for the lines
colors = ['y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y','y']
for xc,c in zip(xcoords,colors):
plt.axvline(x=xc, label='line at x = {}'.format(xc), c=c)
d=1
e=146
plt.text(15+d,e, 'Mart', color='green')
plt.text(46+d,e,'April', color='green')
plt.text(76+d,e, 'Maj', color='green')
plt.text(107+d,e, 'Juni', color='green')
plt.text(137+d,e, 'Juli', color='green')
plt.text(168+d,e,'Avgust', color='green')
plt.text(199+d,e, 'Septemb', color='green')
plt.text(229+d,e, 'Oktobar', color='green')
plt.text(260+d,e, 'Novemb', color='green')
plt.text(290+d,e, 'Decemb', color='green')
plt.text(321+d,e-5, 'Januar\n2021.', color='green')
plt.text(352+d,e, 'Februar', color='green')
plt.text(380+d,e, 'Mart', color='green')
plt.text(411+d,e, 'April', color='green')
plt.text(441+d,e, 'Maj', color='green')
plt.text(472+d,e,'Juni', color='green')
plt.text(502+d,e, 'Juli', color='green')
plt.text(533+d,e, 'Avgust', color='green')
plt.text(564+d,e, 'Septemb', color='green')
plt.text(594+d,e,'Oktobar', color='green')
plt.text(625+d,e, 'Novemb', color='green')
plt.text(655+d,e, 'Decemb', color='green')
plt.text(10,80, 'Source:\n1)WDC-SILSO, Royal Observatory of Belgium, Brussels\n2)NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION,USA\n3)COVID-19 Dashboard by the Center for Systems Science and Engineering (CSSE)\n at Johns Hopkins University (JHU)\n4)Worldometers (http://www.worldometers.info) The Real Time Statistics Project\nCreated by Aleksandar Maričić, December 2021. Konarevo, Serbia', color='g')
plt.grid()
plt.show()
plt.close()
Zaključak i budući pravci
Ovaj program predstavlja pokušaj vizuelne i analitičke evaluacije teorije Čiževskog u savremenom kontekstu pandemije. Iako ne dokazuje uzročno-posledičnu vezu, jasno ukazuje na pojavu korelacija između solarnih i epidemioloških pokazatelja.
Preporučuje se nastavak rada u sledećim pravcima:
- Kvantitativna korelacija i regresiona analiza,
- Spektralna analiza ciklusa i vremenskih pomaka,
- Proširenje na druge bolesti ili geografske regione.
Kvantitativna korelacija
import numpy as np
from scipy.stats import pearsonr
from sklearn.linear_model import LinearRegression
import matplotlib.pyplot as plt
# Pretpostavka: liste podataka su iste dužine, npr:
# sunce, aktivni, novi, letal itd.
dani = []
virusx = []
brzr=[]
dnevno=[]
letalitet=[]
aktivniSx=[]
#aktivni slucajevi u srbiji
aktivniS= [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,2,5,18,24,35,46,47,56,71,88,102,132,168,218,243,285,365,435,478,607,686,727,835,
990,1098,1383,1526,1803,2024,2268,2483,2683,2916,3188,3150,3569,3971,4374,4772,5046,5240,5443,5635,5783,5955,6074,6245,6476,
6704,6904,7069,7259,7487,7641,7747,7720,7786,7754,7617,7482,7281,7087,6893,6668,6423,6249,6066,5912,5789,5667,5669,5595,5531,
5312,5246,5155,5064,5034,4921,4758,4621,4588,4533,4471,4460,4443,4426,4415,4489,437,226,298,367,432,502,575,650,545,601,659,754,
847,939,1032,686,731,775,861,954,1068,1187,1312,1433,1625,1783,1996,2142,2459,2756,2737,2942,3084,3339,3707,3911,4091,4294,
4574,4858,4662,4716,4776,4735,4762,4722,4619,4649,4575,4544,4568,4571,4531,4501,4353,4305,4256,4196,3554,3430,3315,3224,3154,
3096,2999,2873,2817,2454,2220,2128,2361,1947,1897,1612,1662,1612,1411,1361,1222,985,983,924,859,696,747,723,665,714,677,664,
664,597,544,524,530,570,464,398,469,575,419,463,466,546,607,689,756,659,720,800,882,956,1030,1084,1006,1042,1040,1049,1040,
1085,1061,1044,1134,1194,1264,1354,1447,1475,1470,1592,1772,1944,2185,2395,2498,2547,2766,3219,3584,4043,4679,5142,5310,6195,
7421,8738,10131,11703,12949,13486,15137,17335,19394,21350,23515,25211,25950,28016,30938,33938,36384,38878,40976,42244,45421,
49585,54892,59268,62630,65444,68229,72394,77861,84149,89106,92611,95449,98174,102351,106788,111777,114565,115855,115555,115858,
117902,120711,123037,122729,120829,118218,115370,114213,113387,112292,109203,105172,100904,96807,93984,92601,90135,86140,81536,
76836,72861,70318,68559,66559,62749,59303,56140,53945,52710,52058,50160,48298,45641,43345,41615,40557,40131,39453,38068,36225,
34610,34114,33895,33575,32508,31564,30165,29696,29001,29312,29356,28855,28430,27706,27191,27179,27689,28304,28589,28869,28907,
28788,29039,29570,30340,30817,30665,30448,30242,29856,30123,31224,32046,32775,33285,33940,34928,36501,38432,40060,41385,42507,
43316,44857,47392,50062,52597,54858,55910,56391,57850,59984,62056,63695,65106,65738,66376,70982,72841,75076,77615,79452,79980,
80153,81058,82458,84235,86420,87551,87474,91324,86686,89824,92599,93318,93916,93132,91521,89778,88829,87137,86076,85251,83538,
80801,78466,76815,74741,73218,72171,70247,66842,64341,62499,60532,59120,58201,56565,53863,52236,50757,49493,48443,47324,45734,
43152,41247,39579,38137,36921,36130,34582,32452,30507,28913,27576,26408,25501,24218,22642,21081,19761,18756,17933,17336,16490,
15455,14429,13475,12588,11856,11353,10710,9763,8964,8297,7795,7308,6949,6520,5951,5505,5170,4975,5178,4689,4431,4158,4274,3699,
3531,3391,3375,3214,3047,2849,2700,2596,2528,2489,2393,2245,2125,1992,1924,
#juli
1890,1822,1777,1723,1541,1487,1590,1686,1647,1636,
1634,1650,1713,1764,1919,1998,2078,2129,2254,2359,
2513,2663,2788,2925,3018,3156,3347,3572,3785,4069,4249,
#avgust
4405,4666,4933,5217,5629,6070,6426,6692,7216,7781,
8697,9236,10104,10869,11397,12350,13546,14687,16046,17333,
18453,19274,20628,22261,24025,25895,27871,29432,30362,31773,33769,
#septembar
36042,38561,41365,43572,44886,47494,50903,54943,59265,64110,
67732,70518,74441,79711,84899,90188,96035,100444,102716,105793,
109501,113078,116059,119722,121809,122128,123228,125865,127947,130033,
#oktobar
132302,132460,130073,128427,128014,127593,127825,128973,128203,125772,
124274,124722,124961,125552,126591,125900,122513,120804,120914,121387,
122301,124665,125427,123969,122726,123587,124133,125174,126586,126888,125752,
#novembar
131585,138636,118663,119709,118969,116112,112251,109274,106686,104545,
102811,106566,96370,92200,88991,92709,84147,82438,79630,75169,
70516,67164,64474,62305,61096,59084,56190,53260,51444,49889
#decembar
]
#Active Cases
aktivni= [970,1198,1650,2325,3086,4835,6244,7948,9873,11892,14388,17011,20061,23657,27046,29768,32614,34604,36871,38612,39812,52662,56893,58053,58702,59319,59513,59416,58029,56775,55349,54532,52661,51097,49310,47655,45341,44184,43434,43202,42759,43142,43644,45777,48716,51784,55296,60528,66460,75716,87666,101643,115283,131878,149431,169472,193637,221858,255433,283819,315803,354185,390945,432175,481101,534599,588666,636211,681097,738386,793514,844828,903278,956501,1003518,1054262,1098730,1145223,1195889,1259454,1303767,1345539,1387222,1415376,1452098,1485462,1531846,1570911,1601865,1648548,1678109,1716163,1755661,1770913,1807374,1845645,1857650,1886741,1920030,1956453,1997581,2027290,2066649,2100692,2126460,2154228,2196743,2237308,2253969,2275533,2300280,2315046,2330845,2371527,2403384,2433677,2463535,2490843,2520295,2547864,2581210,2559279,2586596,2609953,2621148,2631687,2656842,2673474,2717072,2745317,2729769,2759536,2755737,2707777,2741833,2781064,2819972,2874232,2893968,2939051,2929229,2948480,2991670,3005312,3040257,3062382,3086919,3106799,3139570,3194953,3225775,3242846,3288626,3321958,3351757,3435203,3486451,3556380,3619089,3662900,3706561,3769221,3773175,3846902,3898365,3977063,4034584,4031552,4065024,4127873,4210682,4275018,4359574,4430860,4499162,4537001,4534650,4592166,4661093,4752705,4775817,4806428,4834412,4914195,5007689,5068260,5147442,5173291,5187465,5233042,5268811,5326373,5406051,5469966,5455312,5470019,5488962,5569470,5655397,5739641,5718145,5710013,5712398,5724682,5783813,5840513,5906795,5886197,5852315,5846406,5854453,5899435,5960521,6014422,6041648,5973626,5969266,5963055,6007043,6079440,6120316,6135081,6139027,6134165,6156594,6210699,6238946,6295774,6311442,6276672,6267790,6267611,6309627,6368576,6412511,6429386,6410541,6414882,6435477,6489680,6493652,6529927,6518051,6458415,6435474,6441303,6482181,6533281,6574398,6582944,6554784,6556674,6562418,6615709,6690359,6735099,6739125,6735345,6747105,6804936,6888925,6967624,7093970,7121889,7115621,7155010,7219030,7331414,7432570,7563931,7651336,7716551,7805530,7924139,8101773,8311069,8509291,8669515,8752333,8908475,9100420,9340190,9597747,9818924,9979497,10111845,10261755,10456951,10719867,10995429,11275765,11488970,11622707,11805151,12059203,12097361,12349936,12533318,12700629,12766394,12785132,12913091,13087969,13280886,13408461,13502108,13538507,13598830,13574552,13692467,13729008,13800216,13841900,13778868,13782803,13806976,13924469,14059191,14132025,14228763,14207001,14232198,14267910,14383806,14478352,14576481,14683463,14670582,14704341,14784205,14950318,15155326,15226012,15359350,15321897,15353635,15449781,15585023,15686928,15643989,15626741,15530905,15556056,15673838,15894282,16112378,16143981,16246608,16124541,16285182,16489839,16786864,17142460,17369167,17583856,17618351,17709663,17904294,18051020,18216598,18363423,18454632,18402513,18263096,18275931,18367221,18488615,18577450,18619842,18435525,18338852,18366141,18338598,18374207,18376094,18365924,18077103,17926104,17800819,17733856,17701044,17591304,17489597,17257193,17062578,16867256,16771901,16674035,16578826,16446487,16229666,16034669,15902740,15791153,15715449,15621888,15532321,15332585,15186511,15119273,15082751,15057025,14976731,14904579,14750399,14645535,14656801,14616794,14614324,14572361,14568917,14403324,14335344,14363665,14391068,14449748,14498509,14510923,14429668,14410727,14481252,14519425,14627875,14730356,14791007,14692201,14639221,14678743,14786384,14950130,15094304,15191773,15146801,15159968,15269960,15440435,15619293,15698377,15769442,15715938,15734355,15832994,16005721,16217432,16376454,16472496,16458179,16543805,16709455,16900315,17085015,17251677,17307768,17264832,17327568,17435462,17586326,17748780,17841683,17910238,17771554,17774769,17835250,17922227,17960591,17918121,17885748,17734096,17606583,17614255,17629735,17680331,17598013,17521216,17312331,17191421,17092209,17017616,16913927,16718074,16530353,16234928,15983994,15846250,15711746,15589897,15418316,15286477,14985183,14775751,14618911,14488092,14351687,14185703,14032404,13795090,13541103,13373570,13273349,13186428,13034769,12867075,12599050,12405386,12283053,12213865,12172463,12007228,11926500,11763839,11663048,11594641,11579044,11552910,11520419,11467194,11337205,11284637,11308516,11377614,11438818,11439120,11439033,11382991,11339799,11356605,11416559,11485828,11532587,11564424,11516202,11518751,11597248,11703738,11823819,11906067,11930367,11915786,12008068,12181865,12383580,12586814,12755670,12883844,12916679,13048350,13196798,13362822,13512030,13696765,13855114,13885610,14016656,14223446,14463317,14699410,14887024,15039923,15096578,15236003,15462088,15685228,15904298,16062619,16173353,16152520,16194062,16294147,16426295,16639082,16758533,16832253,16797065,16869978,17007821,17205935,17409917,17536921,17632329,17584317,17644645,17804944,17974838,18165948,18282737,18367158,18319522,18355841,18403887,18534851,18681800,18727018,18759376,18667573,18601900,18584058,18493386,18518118,18554068,18556867,18390032,18297975,18285333,18343679,18409677,18409287,18373074,18226371,18168150,18143319,18161380,18234964,18224028,18198455,18068979,17953864,17919505,17931995,17937631,17895000,17821643,17604403,17515860,17466831,17487844,17479116,17493411,17471920,17378245,17279243,17288559,17338257,17375501,17411941,17421480,17325955,17282503,17334617,17412513,17460143,17509207,17539416,17435219,17457139,17500254,17604518,17691366,17769908,17821242,17765795,17769065,17803803,17917085,18041046,18139124,18191603,18131086,18146757,18253585,18415428,18515330,18604553,18664845,18663599,18713078,18816260,18994434,19142890,19256711,19339780,19375181,19479927,19625367,19801102,19961406,20068615,20158138,20154273,20262105,20473352,20716975
]
#Daily New Cases
novi= [ 0,271,475,701,787,1784,1479,1764,2016,2137,2626,2857,3253,3927,3728,3184,3453,2685,3004,2569,2057,14180,5174,2682,2132,2158,2031,
1880,534,1034,1058,1038,628,993,861,1136,1459,1818,2204,2633,2613,3304,3165,4318,5049,5739,5846,7208,8772,11274,14375,16659,
17388,18828,20398,23894,28017,32093,38443,33976,37002,43723,46280,49842,62399,67213,67779,61190,64194,76150,78257,79299,86756,
82180,74285,75876,83711,89070,89821,98041,85764,76721,76413,80436,87526,87878,90887,85362,78952,83551,82335,84635,88708,97192,
91697,75773,71555,79208,88919,89018,95833,83454,82611,81591,84120,97217,97135,97297,88991,80837,73811,89544,92625,98635,102956,
97515,84337,92207,99219,106270,109469,110005,103039,98727,92237,95770,110094,120262,129491,126924,111485,103732,120308,123952,
134316,133883,131626,117295,110283,124932,140057,141964,145070,138014,126872,128676,148797,151080,146094,186061,162746,134578,
143513,169230,179814,186426,199399,184428,168349,163724,183517,203893,216184,219183,201083,180733,176383,216285,220750,231078,
242961,222981,202034,196468,228147,241917,253913,245375,232751,223776,205128,246407,285833,280269,294173,268444,224832,218432,
255716,295752,292129,295847,265168,224552,202280,260611,278348,287922,287574,277217,227151,220013,274447,294745,291053,294881,
270485,221760,205224,265196,280622,276760,268924,272740,217425,219774,262589,281769,282032,294910,269203,230619,250890,268201,
292601,294225,311490,282708,244357,206785,252239,295262,307175,322363,296175,258503,250632,289681,312068,318811,328653,304359,
259701,239506,287471,317960,319629,328970,306967,262928,238878,295278,322302,326924,333038,305021,261140,272417,316425,352800,
360979,365346,378799,295305,275838,324630,387724,404393,419920,402998,349454,338321,396229,447454,485743,495541,485560,435537,
400954,472381,518212,549976,575070,513186,472954,454347,504326,574860,625363,629281,640307,507881,472096,571802,626796,654267,
661424,614268,521646,492160,577526,622543,665064,669388,618514,527404,528768,573774,643213,626543,610496,600876,528147,491282,
592630,646356,693061,694940,654953,553718,518730,613601,660833,702769,713235,666320,553963,526988,610223,726902,738084,721570,
647672,564763,535794,623750,698426,698329,543326,472193,449396,495063,642932,738268,762421,649672,569293,544878,557670,719985,
807275,843545,844898,773450,645450,588370,687420,745635,752369,762968,680151,560558,477222,595085,663842,652312,640234,604667,
484624,437251,534434,589635,599894,584225,531774,418152,390109,456799,485896,507390,496926,443125,363397,319842,389735,441946,
444068,428673,387688,305055,262514,346460,397316,402393,412471,388327,318279,285206,378757,444476,449080,436634,398230,322118,
294621,372220,445991,450484,454005,414685,379675,292509,394273,468872,482114,494290,454141,378036,336539,456070,535036,552431,
558259,519355,437684,423754,505529,590719,635047,634409,595760,503499,456782,549425,646455,706818,652554,568382,552928,480853,
632412,690002,746649,791909,723634,654460,584249,743399,813246,843245,837432,806207,731013,656552,830438,887727,889544,901831,
846750,746650,671814,837361,892376,904019,876155,818457,698126,670010,785675,849818,860246,841621,798261,667044,608270,717345,
756456,747868,700843,648839,550306,535468,618071,664346,657090,625307,584828,491074,445076,525390,562678,538379,510597,502832,
415386,367697,450417,492556,476999,421839,411709,340060,314194,365250,423996,438400,416647,382577,310599,302929,373620,401756,
390942,405718,368933,305291,280787,378313,434421,406864,413618,382477,323550,318371,384510,398613,434322,441876,399218,355040,
347971,435087,464579,489155,497078,450061,402762,399693,515841,557405,568097,567520,527506,495069,433338,521229,566413,573085,
584084,547288,495771,463827,606634,665746,677105,654360,598016,548356,500144,625418,694824,716583,708209,643466,570749,522696,
659288,708573,723819,734453,649807,565633,531676,673022,710262,746531,723609,639886,565388,526593,680542,737882,736713,728053,
642787,561297,536450,640042,687170,694941,679936,585025,541229,499275,540986,613986,628787,609981,553517,488574,448934,525515,
574921,586651,576582,495293,428522,412017,486196,533739,525027,513626,442844,398583,382667,439113,492957,501552,481363,410557,
358295,347984,422971,458848,470740,454075,396523,353325,332467,403434,446998,453966,441840,391908,347717,353049,423089,458848,
472178,462835,418013,361827,341166,440580,480623,489868,475655,429179,371904,363176,407193,489067,526668,512101,464432,393084,
388611,479162,553103,564281,538638,490566,416480,429661,517476,600370,623858,603772,556439,461154,470739,587836,640658,636805,
619317,542458,462875,477012,611412,682526,694461
]
letal= [142,106,98,136,117,121,113,100,158,81,64,37,58,65,54,73,
67,85,83,103,107,106,228,198,274,331,361,455,418,706,653,839,1002,1125,1417,1668,1717,1986,2609,2633,3154,3571,3858,3555,4329,
4806,5443,6439,6291,6428,5407,5826,7901,7063,8010,7408,6586,5952,6014,7662,8473,7266,8819,7009,5352,6101,7709,7013,7188,6773,
6700,4543,5228,7445,7457,6375,6612,6314,4519,5343,6662,7364,6419,6202,5463,5147,4630,6482,5905,5971,5815,5008,4070,4502,5950,
5412,5805,5549,4846,4130,4454,4708,5737,5333,5468,4832,4134,4115,5609,5650,5655,5326,4923,4405,4218,5637,5872,5563,5432,5125,
4328,4554,7430,5902,5903,5823,5051,4426,4051,5871,5504,5597,5376,5107,4240,4720,5756,5542,5664,5684,5206,4292,4569,6216,5937,
6075,5956,5662,5047,4831,6343,6361,6631,6316,5773,5135,5048,6734,7576,6863,6868,6315,5090,5310,6489,7229,6935,6767,6182,5011,
5391,6861,7363,7031,6961,6022,5376,5314,6727,6962,7003,6448,6031,5135,5190,6877,6954,6630,6599,6084,5031,5025,6650,6599,6457,
6232,5688,4695,4879,6394,6509,6160,6078,5291,4596,4511,5004,6115,5913,5907,5240,4338,4770,6288,5971,5662,5799,5165,4311,4193,
5744,5816,5431,5504,5271,4082,3928,5764,5686,5616,5689,4969,4321,4697,5829,6002,6505,5914,5337,4659,4216,5257,6208,6142,6365,
5829,4313,4931,6503,6915,6568,6659,6009,4853,5616,7376,7249,7233,7656,6960,5912,6375,8633,9529,9088,9491,8094,6722,7437,9711,
10338,9943,10125,9712,7546,8139,10964,11966,11368,11374,9623,8354,8885,12311,12401,11407,11225,10027,8214,9290,12556,12616,
12786,12507,10814,8479,9185,12439,12581,12973,12658,11322,8590,9740,13437,13965,13498,13106,11499,8993,10508,13763,13731,12271,
9505,8089,8614,10395,14807,15558,14130,10567,9067,8499,10515,14739,15024,15105,15361,13165,9867,10617,16619,16893,16011,15528,
14016,10043,10558,16050,17474,16992,15987,14743,10398,11059,17024,17520,16856,15264,13170,9731,10843,15533,15411,14326,14242,
11652,8228,9482,13661,13796,13174,12188,10558,7314,7368,10393,11189,11341,11189,8871,6924,7172,10823,10665,10572,9855,8462,6579,
7207,9947,10734,10137,9757,8107,6112,7094,9168,10038,9815,9556,8376,6181,7278,10291,10466,10160,10530,8619,6320,7629,10885,10419,
10764,11629,10128,7236,8081,11353,12217,11824,10651,9189,7626,8097,12467,13257,14025,13557,11442,8999,9574,13278,13838,14266,
12969,12134,10096,10644,14712,14315,13845,14715,14139,10540,11518,15651,15671,15854,14676,13957,10877,11627,14770,15287,14623,
14535,13647,11045,11650,14597,14645,14532,14166,13397,10727,11597,14891,13749,14088,13650,11749,10633,9630,12897,12805,11976,
12100,11058,8645,9056,11170,11377,11131,10567,9452,7840,7981,10355,10274,10232,9499,8711,6968,6843,9294,9518,8802,9116,8806,6890,
6511,8980,9141,8714,8791,7731,6415,6408,7950,8833,8365,8589,7396,6364,6374,8290,8501,8925,8527,7675,6643,6566,8212,8720,8615,8767,
7391,7115,6991,8542,8712,9023,8782,8523,7189,7646,9618,10278,10565,9512,9256,8086,8366,10341,10195,10603,10347,9714,8576,8408,
11036,10723,11015,10511,9402,8894,8304,10574,11074,11509,10789,9667,9170,8154,11073,11856,11350,10563,9762,8388,8303,9750,10980,
11317,10425,8948,7632,7540,9095,10251,10309,9620,8954,7153,7395,9489,10768,9862,8976,7908,6812,6315,8800,9731,9199,8909,7074,
6028,5955,8660,9236,8315,7701,6749,5549,5429,7877,8578,8115,7915,6434,5062,5207,7122,7891,7864,7302,6248,4989,5338,7462,7664,
7651,8012,6538,5357,5611,7857,9021,8267,7896,6670,5164,5686,7336,8025,7763,7896,6972,5178,5900,8012,8570,7594,7876,6725,5162,
5728,7786,8611,8392,7941,6598,4873,6026,8467,8422,7658,7213,6428,5006,5856,8122]
sunce=[ #259
#15 februar 2020
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
#mart 2020 -31
0,0,0,0,0,0,2,16,11,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,3,11,
#april 2020-30
13,13,13,13,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6,13,26,15,24,20,
#maj - 31
4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,
#juni -30
6,0,9,11,13,16,16,16,14,12,11,11,11,11,8,0,0,0,0,0,0,0,0,0,0,6,4,0,0,0,
#juli -31
4,2,0,7,5,5,8,0,0,0,0,0,0,0,2,0,0,0,0,0,6,11,11,11,11,11,11,20,21,21,21,
#avgust -31
26,15,11,11,12,14,17,12,13,13,12,17,10,5,0,0,0,13,16,12,3,0,0,0,0,0,0,0,0,0,0,
#septembar-30
0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,7,5,4,0,0,0,0,0,
#oktobar -31
0,0,0,0,0,0,0,6,20,18,20,14,0,4,13,13,14,21,17,14,14,12,17,18,19,22,41,35,42,34,26,
#novembar -30
5,9,16,26,31,41,38,44,29,29,29,32,26,20,5,0,10,13,13,13,26,34,48,44,53,58,75,86,96,87,
#decembar -31
56,48,45,41,37,25,21,14,14,12,12,11,11,13,20,14,13,7,0,0,12,12,24,28,31,35,33,30,32,32,34,
#2021
#januar - 31
24,17,0,0,0,0,0,0,0,0,0,0,0,3,14,12,14,12,20,21,25,35,32,23,27,17,20,7,0,0,0,
#februar 28
0,9,7,0,0,0,0,2,2,0,0,0,0,0,0,0,0,10,9,9,10,16,36,38,34,18,17,13,
#mart 31
10,16,35,30,13,7,21,14,15,17,22,14,11,23,24,19,13,13,13,11,8,22,27,30,27,25,19,12,12,9,0,
#april 30
0,0,4,12,11,6,0,0,0,0,10,14,19,21,25,35,15,18,36,57,46,44,37,54,55,50,55,46,37,28,
#maj 31
10,0,0,0,0,0,10,17,20,34,32,33,30,26,28,13,14,28,27,20,14,19,27,31,41,41,41,31,15,26,30,
#juni 30
22,29,31,35,38,38,49,34,25,27,19,8,15,12,11,11,12,21,15,14,13,16,12,11,23,19,33,46,56,54,
#juli 31
57,61,61,51,44,50,20,17,12,16,22,23,19,29,22,35,50,48,49,46,72,75,55,31,36,31,21,7,4,0,2,
#avgust 31
8,13,17,17,24,9,0,0,7,0,19,8,10,20,13,20,15,13,22,13,17,19,17,21,35,48,70,75,51,43,40,
#septembar 30
38,33,25,70,75,83,74,98,102,97,74,50,34,23,10,0,0,0,13,44,65,81,69,61,46,50,49,56,70,45,
#oktobar 31
36,34,26,35,31,26,16,19,24,39,30,18,20,21,12,11,0,18,13,12,18,37,50,41,68,92,104,100,85,78,68,
#novembar
51,43,33,26,35,34,28,39,45,39,41,35,27,20,23,32,28,22,22,21,21,23,32,34,26,40,38,45,41,54
]
n = len(sunce)
# Normalizacije ili transformacije po tvom primeru:
brzr = np.array([aktivni[t]/130000 for t in range(n)]) # aktivni slučajevi u svetu
dnevno = np.array([novi[t]/8000 for t in range(n)]) # novozaraženi u svetu
letalitet = np.array([letal[t]/300 for t in range(n)]) # letalitet
aktivniSx = np.array([aktivniS[t]/1000 for t in range(n)]) # aktivni slučajevi u Srbiji
sunce_arr = np.array(sunce)
# --- Korelacije ---
def print_corr(x, y, name_x, name_y):
corr, p_value = pearsonr(x, y)
print(f"Pearsonova korelacija između {name_x} i {name_y}: {corr:.4f} (p={p_value:.4g})")
print_corr(sunce_arr, brzr, "Sunčeve pege", "Aktivni slučajevi u svetu")
print_corr(sunce_arr, dnevno, "Sunčeve pege", "Novozaraženi u svetu")
print_corr(sunce_arr, letalitet, "Sunčeve pege", "Letalitet")
print_corr(sunce_arr, aktivniSx, "Sunčeve pege", "Aktivni slučajevi u Srbiji")
# --- Linearna regresija ---
# Cilj: predvideti broj aktivnih slučajeva u svetu na osnovu broja sunčevih pega
X = sunce_arr.reshape(-1, 1) # prediktor mora biti 2D
y = brzr
model = LinearRegression()
model.fit(X, y)
y_pred = model.predict(X)
print(f"\nLinearni model: aktivni_slučajevi = {model.coef_[0]:.6f} * sunčeve_pege + {model.intercept_:.6f}")
print(f"R^2 (koeficijent determinacije): {model.score(X, y):.4f}")
# --- Grafički prikaz ---
plt.figure(figsize=(10,6))
plt.scatter(sunce_arr, brzr, label='Podaci', alpha=0.5)
plt.plot(sunce_arr, y_pred, color='red', label='Linearni fit')
plt.xlabel('Broj sunčevih pega')
plt.ylabel('Aktivni slučajevi u svetu (normalizovani)')
plt.title('Linearni model: Aktivni slučajevi vs. Sunčeve pege')
plt.legend()
plt.grid(True)
plt.show()
Rezultat:
korelacija.py Pearsonova korelacija između Sunčeve pege i Aktivni slučajevi u svetu: 0.4971 (p=3.613e-42) Pearsonova korelacija između Sunčeve pege i Novozaraženi u svetu: 0.4305 (p=6.188e-31) Pearsonova korelacija između Sunčeve pege i Letalitet: 0.2838 (p=1.353e-13) Pearsonova korelacija između Sunčeve pege i Aktivni slučajevi u Srbiji: 0.4400 (p=2.159e-32) Linearni model: aktivni_slučajevi = 1.224938 * sunčeve_pege + 57.430256 R^2 (koeficijent determinacije): 0.2471
1. Korelacija
Pearsonov koeficijent korelacije meri linearnu povezanost između dve varijable i kreće se od -1 do +1.
Ovde su dobijene pozitivne korelacije između broja sunčevih pega i svih analiziranih COVID-19 indikatora:
- Aktivni slučajevi u svetu: 0.4971 — umereno jaka pozitivna korelacija
- Novozaraženi u svetu: 0.4305 — umerena pozitivna korelacija
- Letalitet: 0.2838 — slaba do umerena pozitivna korelacija
- Aktivni slučajevi u Srbiji: 0.4400 — umerena pozitivna korelacija
Sve p-vrednosti su ekstremno male (daleko ispod 0.05), što znači da su ove korelacije statistički značajne — vrlo mala je verovatnoća da su dobijene slučajno.
2. Linearni regresioni model
Model za predviđanje aktivnih slučajeva u svetu na osnovu broja sunčevih pega je:
$$\hat{aktivni\_slucajevi} = 1.2249 \times sunceve\_pege + 57.4303$$
Koeficijent \(R^2 = 0.2471\) znači da model objašnjava oko 24.7% varijanse aktivnih slučajeva na osnovu broja sunčevih pega.
Ovo nije naročito visok procenat, što znači da postoji mnogo drugih faktora koji utiču na broj aktivnih slučajeva i da model nije savršen.
Regresiona analiza
OLS Regression Results
==============================================================================
Dep. Variable: sunce R-squared: 0.251
Model: OLS Adj. R-squared: 0.248
Method: Least Squares F-statistic: 72.87
Date: Sun, 06 Jul 2025 Prob (F-statistic): 1.21e-40
Time: 08:31:29 Log-Likelihood: -2806.7
No. Observations: 655 AIC: 5621.
Df Residuals: 651 BIC: 5639.
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 4.0564 1.709 2.374 0.018 0.701 7.411
aktivni 1.713e-06 2.28e-07 7.518 0.000 1.27e-06 2.16e-06
novi 8.62e-07 6.74e-06 0.128 0.898 -1.24e-05 1.41e-05
letal -0.0005 0.000 -1.857 0.064 -0.001 2.99e-05
==============================================================================
Omnibus: 185.861 Durbin-Watson: 0.194
Prob(Omnibus): 0.000 Jarque-Bera (JB): 502.272
Skew: 1.418 Prob(JB): 8.57e-110
Kurtosis: 6.218 Cond. No. 3.03e+07
==============================================================================
Korelacija i regresiona analiza
Pearsonov koeficijent korelacije meri linearnu povezanost između dve varijable i kreće se od -1 do +1.
Ovde su dobijene pozitivne korelacije između broja sunčevih pega i svih analiziranih COVID-19 indikatora:
- Aktivni slučajevi u svetu: \( r = 0.4971 \)
- Novozaraženi u svetu: \( r = 0.4305 \)
- Letalitet: \( r = 0.2838 \)
- Aktivni slučajevi u Srbiji: \( r = 0.4400 \)
Sve p-vrednosti su ekstremno male (\( p \ll 0.05 \)), što znači da su ove korelacije statistički značajne.
Linearni regresioni model
Model za predviđanje broja sunčevih pega na osnovu epidemioloških podataka:
\[ \text{sunčeve_pege} = 4.056 + 1.713 \times 10^{-6} \cdot \text{aktivni} – 0.0005 \cdot \text{letalitet} \]
Koeficijent determinacije je \( R^2 = 0.251 \), što znači da model objašnjava oko 25% varijanse broja pega.
Grangerova analiza kauzalnosti
Sa vremenskim zaostatkom od 4 dana, broj aktivnih slučajeva statistički Granger-uzrokuje broj pega:
\( p = 0.0435 \), \( \chi^2 = 10.03 \)
Zaključak
Postoji umerena, statistički značajna pozitivna veza između aktivnosti Sunca i ključnih pandemijskih indikatora kao što su:
- broj aktivnih slučajeva,
- broj novozaraženih,
- letalitet,
- i broj slučajeva u Srbiji.
Ipak, ova veza:
- nije dovoljno jaka za precizno predviđanje,
- ne implicira uzročnost u fizičkom smislu.
U analizi nisu uzeti u obzir svi relevantni faktori. Na primer, vremenske prilike imaju snažan uticaj:
- U zimskim i kišnim uslovima ljudi više borave u zatvorenom, što olakšava širenje virusa.
- U letnjim mesecima, na suvom i toplom vremenu, ljudi češće borave na otvorenom, gde je transmisija virusa značajno smanjena.
Takvi sezonski faktori mogu zamagliti ili pojačati uticaj Sunčeve aktivnosti.
Preporuka: Uključiti dodatne varijable u modele (klimatske, društvene, biološke) i sprovesti napredne regresione i vremenske analize radi dubljeg razumevanja povezanosti.
Naučne reference i literatura
- Čiževski A. L. (1976). Zemnoe ekho solnechnykh bur’ [Земное эхо солнечных бурь]. Moskva: Mysl’.
(Originalna teorija o povezanosti solarne aktivnosti sa društvenim i biološkim procesima.)
https://www.rulit.me/books/zemnoe-eho-solnechnyh-bur-download-163052.html - Palmer, S. J., Rycroft, M. J., & Cermack, M. (2006). Solar and geomagnetic activity, extremely low frequency magnetic and electric fields and human health at the Earth’s surface. Surveys in Geophysics, 27(5), 557–595.
https://doi.org/10.1007/s10712-006-9010-7 - Zhadin, M. N. (2001). Review of Russian literature on biological action of DC and low-frequency AC magnetic fields. Bioelectromagnetics, 22(1), 27–45.
(Pregled eksperimenata o uticaju geomagnetnih polja na ćelijski metabolizam.) - Cherry, N. (2002). Schumann Resonances, a plausible biophysical mechanism for the human health effects of solar/geomagnetic activity.
Natural Hazards, 26, 279–331. https://doi.org/10.1023/A:1015614096609 - Stoupel, E. (2002). The effect of geomagnetic activity on cardiovascular parameters. Bioelectromagnetics, 23(6), 531–540.
- Thakur, K. K., & Kour, R. (2021). Can solar activity influence the pandemic? Correlation between solar indices and COVID-19 cases. Current Science, 120(10), 1563–1565.
(Studija o pokušaju korelacije pandemije COVID-19 i solarnih faktora.) - SILSO Data – WDC-SILSO, Royal Observatory of Belgium.
https://www.sidc.be/SILSO/ - Johns Hopkins University (CSSE) – COVID-19 Dashboard
https://coronavirus.jhu.edu/map.html - Worldometers COVID-19 – Real-time statistics
https://www.worldometers.info/coronavirus/