PMC:7029158 / 9217-11669
Annnotations
{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7029158","sourcedb":"PMC","sourceid":"7029158","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7029158","text":"Parameter estimation process\nUnder the gradually enhanced control strategies since January 23rd, 2020, the parameter values with substantial changes include the contact rate, the diagnose rate and the quarantined rate q. Therefore, we fixed the parameter values except these three as the estimated values in our previous study (Tang et al., 2020). The initial contact rate c0 is assumed to be the average contact rate between January 10th, 2020 and January 22nd, 2020, hence c0=14.781. With the same assumption, we set δI0=0.133. Note that, the initial conditions can be obtained by solving our previous model (Tang et al., 2020) from January 10th, 2020 to January 23rd, 2020. Thus, the main task is to estimate the parameter values q,cb,r1,δIf,r2.\nWe use the Markov Chain Monte Carlo (MCMC) method to fit the model to the data, and adopt an adaptive Metropolis-Hastings (M-H) algorithm to carry out the MCMC procedure. The algorithm is run for 70,000 iterations with a burn-in of the first 50,000 iterations, and the Geweke convergence diagnostic method is employed to assess convergence of chains. The estimation results are given in Table 1 .\nTable 1 Parameter values.\nParameter Definitions Estimated mean value Standard deviation Data source\nc0 Contact rate at the initial time 14.781 0.904 1\ncb Minimum contact rate under the current control strategies 2.9253 0.5235 MCMC\nr1 Exponential decreasing rate of contact rate 1.3768 0.283 MCMC\nβ Probability of transmission per contact 2.1011×10−8 1.1886×10−9 1\nq Quarantined rate of exposed individuals 1.2858×10−5 3.1488×10−6 MCMC\nσ Transition rate of exposed individuals to the infected class 1/7 – 2\nλ Rate at which the quarantined uninfected contacts were released into the wider community 1/14 – 3,4\nϱ Probability of having symptoms among infected individuals 0.86834 0.049227 1\nδI0 Initial transition rate of symptomatic infected individuals to the quarantined infected class 0.13266 0.021315 1\n1/δIf The shortest period of diagnosis 0.3654 0.1431 MCMC\nr2 Exponential decreasing rate of diagnose rate 0.3283 0.0225 MCMC\nδq Transition rate of quarantined exposed individuals to the quarantined infected class 0.1259 0.052032 1\nγI Recovery rate of symptomatic infected individuals 0.33029 0.052135 1\nγA Recovery rate of asymptomatic infected individuals 0.13978 0.034821 1\nγH Recovery rate of quarantined infected individuals 0.11624 0.038725 1\nα Disease-induced death rate 1.7826×10−5 6.8331×10−6 1","divisions":[{"label":"title","span":{"begin":0,"end":28}},{"label":"p","span":{"begin":29,"end":748}},{"label":"label","span":{"begin":1146,"end":1153}},{"label":"caption","span":{"begin":1154,"end":1171}},{"label":"p","span":{"begin":1154,"end":1171}},{"label":"tr","span":{"begin":1172,"end":1245}},{"label":"th","span":{"begin":1172,"end":1181}},{"label":"th","span":{"begin":1182,"end":1193}},{"label":"th","span":{"begin":1194,"end":1214}},{"label":"th","span":{"begin":1215,"end":1233}},{"label":"th","span":{"begin":1234,"end":1245}},{"label":"tr","span":{"begin":1246,"end":1296}},{"label":"td","span":{"begin":1246,"end":1248}},{"label":"td","span":{"begin":1249,"end":1281}},{"label":"td","span":{"begin":1282,"end":1288}},{"label":"td","span":{"begin":1289,"end":1294}},{"label":"td","span":{"begin":1295,"end":1296}},{"label":"tr","span":{"begin":1297,"end":1376}},{"label":"td","span":{"begin":1297,"end":1299}},{"label":"td","span":{"begin":1300,"end":1357}},{"label":"td","span":{"begin":1358,"end":1364}},{"label":"td","span":{"begin":1365,"end":1371}},{"label":"td","span":{"begin":1372,"end":1376}},{"label":"tr","span":{"begin":1377,"end":1441}},{"label":"td","span":{"begin":1377,"end":1379}},{"label":"td","span":{"begin":1380,"end":1423}},{"label":"td","span":{"begin":1424,"end":1430}},{"label":"td","span":{"begin":1431,"end":1436}},{"label":"td","span":{"begin":1437,"end":1441}},{"label":"tr","span":{"begin":1442,"end":1509}},{"label":"td","span":{"begin":1442,"end":1443}},{"label":"td","span":{"begin":1444,"end":1483}},{"label":"td","span":{"begin":1484,"end":1495}},{"label":"td","span":{"begin":1496,"end":1507}},{"label":"td","span":{"begin":1508,"end":1509}},{"label":"tr","span":{"begin":1510,"end":1580}},{"label":"td","span":{"begin":1510,"end":1511}},{"label":"td","span":{"begin":1512,"end":1551}},{"label":"td","span":{"begin":1552,"end":1563}},{"label":"td","span":{"begin":1564,"end":1575}},{"label":"td","span":{"begin":1576,"end":1580}},{"label":"tr","span":{"begin":1581,"end":1651}},{"label":"td","span":{"begin":1581,"end":1582}},{"label":"td","span":{"begin":1583,"end":1643}},{"label":"td","span":{"begin":1644,"end":1647}},{"label":"td","span":{"begin":1648,"end":1649}},{"label":"td","span":{"begin":1650,"end":1651}},{"label":"tr","span":{"begin":1652,"end":1753}},{"label":"td","span":{"begin":1652,"end":1653}},{"label":"td","span":{"begin":1654,"end":1742}},{"label":"td","span":{"begin":1743,"end":1747}},{"label":"td","span":{"begin":1748,"end":1749}},{"label":"td","span":{"begin":1750,"end":1753}},{"label":"tr","span":{"begin":1754,"end":1832}},{"label":"td","span":{"begin":1754,"end":1755}},{"label":"td","span":{"begin":1756,"end":1813}},{"label":"td","span":{"begin":1814,"end":1821}},{"label":"td","span":{"begin":1822,"end":1830}},{"label":"td","span":{"begin":1831,"end":1832}},{"label":"tr","span":{"begin":1833,"end":1949}},{"label":"td","span":{"begin":1833,"end":1836}},{"label":"td","span":{"begin":1837,"end":1930}},{"label":"td","span":{"begin":1931,"end":1938}},{"label":"td","span":{"begin":1939,"end":1947}},{"label":"td","span":{"begin":1948,"end":1949}},{"label":"tr","span":{"begin":1950,"end":2007}},{"label":"td","span":{"begin":1950,"end":1955}},{"label":"td","span":{"begin":1956,"end":1988}},{"label":"td","span":{"begin":1989,"end":1995}},{"label":"td","span":{"begin":1996,"end":2002}},{"label":"td","span":{"begin":2003,"end":2007}},{"label":"tr","span":{"begin":2008,"end":2074}},{"label":"td","span":{"begin":2008,"end":2010}},{"label":"td","span":{"begin":2011,"end":2055}},{"label":"td","span":{"begin":2056,"end":2062}},{"label":"td","span":{"begin":2063,"end":2069}},{"label":"td","span":{"begin":2070,"end":2074}},{"label":"tr","span":{"begin":2075,"end":2180}},{"label":"td","span":{"begin":2075,"end":2077}},{"label":"td","span":{"begin":2078,"end":2162}},{"label":"td","span":{"begin":2163,"end":2169}},{"label":"td","span":{"begin":2170,"end":2178}},{"label":"td","span":{"begin":2179,"end":2180}},{"label":"tr","span":{"begin":2181,"end":2252}},{"label":"td","span":{"begin":2181,"end":2183}},{"label":"td","span":{"begin":2184,"end":2233}},{"label":"td","span":{"begin":2234,"end":2241}},{"label":"td","span":{"begin":2242,"end":2250}},{"label":"td","span":{"begin":2251,"end":2252}},{"label":"tr","span":{"begin":2253,"end":2325}},{"label":"td","span":{"begin":2253,"end":2255}},{"label":"td","span":{"begin":2256,"end":2306}},{"label":"td","span":{"begin":2307,"end":2314}},{"label":"td","span":{"begin":2315,"end":2323}},{"label":"td","span":{"begin":2324,"end":2325}},{"label":"tr","span":{"begin":2326,"end":2397}},{"label":"td","span":{"begin":2326,"end":2328}},{"label":"td","span":{"begin":2329,"end":2378}},{"label":"td","span":{"begin":2379,"end":2386}},{"label":"td","span":{"begin":2387,"end":2395}},{"label":"td","span":{"begin":2396,"end":2397}},{"label":"td","span":{"begin":2398,"end":2399}},{"label":"td","span":{"begin":2400,"end":2426}},{"label":"td","span":{"begin":2427,"end":2438}},{"label":"td","span":{"begin":2439,"end":2450}}],"tracks":[{"project":"LitCovid-PD-MONDO","denotations":[{"id":"T21","span":{"begin":970,"end":974},"obj":"Disease"}],"attributes":[{"id":"A21","pred":"mondo_id","subj":"T21","obj":"http://purl.obolibrary.org/obo/MONDO_0043519"},{"subj":"T21","pred":"source","obj":"LitCovid-PD-MONDO"}]},{"project":"LitCovid-PD-CLO","denotations":[{"id":"T51","span":{"begin":738,"end":740},"obj":"http://purl.obolibrary.org/obo/CLO_0008697"},{"id":"T52","span":{"begin":738,"end":740},"obj":"http://purl.obolibrary.org/obo/CLO_0052381"},{"id":"T53","span":{"begin":872,"end":875},"obj":"http://purl.obolibrary.org/obo/CLO_0007706"},{"id":"T54","span":{"begin":968,"end":969},"obj":"http://purl.obolibrary.org/obo/CLO_0001020"},{"id":"T55","span":{"begin":1377,"end":1379},"obj":"http://purl.obolibrary.org/obo/CLO_0008697"},{"id":"T56","span":{"begin":1377,"end":1379},"obj":"http://purl.obolibrary.org/obo/CLO_0052381"},{"id":"T57","span":{"begin":1743,"end":1747},"obj":"http://purl.obolibrary.org/obo/CLO_0053001"},{"id":"T58","span":{"begin":2254,"end":2255},"obj":"http://purl.obolibrary.org/obo/CLO_0001020"}],"attributes":[{"subj":"T51","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T52","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T53","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T54","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T55","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T56","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T57","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T58","pred":"source","obj":"LitCovid-PD-CLO"}]},{"project":"LitCovid-sentences","denotations":[{"id":"T51","span":{"begin":0,"end":28},"obj":"Sentence"},{"id":"T52","span":{"begin":29,"end":220},"obj":"Sentence"},{"id":"T53","span":{"begin":221,"end":347},"obj":"Sentence"},{"id":"T54","span":{"begin":348,"end":485},"obj":"Sentence"},{"id":"T55","span":{"begin":486,"end":529},"obj":"Sentence"},{"id":"T56","span":{"begin":530,"end":676},"obj":"Sentence"},{"id":"T57","span":{"begin":677,"end":748},"obj":"Sentence"},{"id":"T58","span":{"begin":749,"end":919},"obj":"Sentence"},{"id":"T59","span":{"begin":920,"end":1099},"obj":"Sentence"},{"id":"T60","span":{"begin":1100,"end":1145},"obj":"Sentence"},{"id":"T61","span":{"begin":1146,"end":1171},"obj":"Sentence"},{"id":"T62","span":{"begin":1172,"end":1245},"obj":"Sentence"},{"id":"T63","span":{"begin":1246,"end":1296},"obj":"Sentence"},{"id":"T64","span":{"begin":1297,"end":1376},"obj":"Sentence"},{"id":"T65","span":{"begin":1377,"end":1441},"obj":"Sentence"},{"id":"T66","span":{"begin":1442,"end":1509},"obj":"Sentence"},{"id":"T67","span":{"begin":1510,"end":1580},"obj":"Sentence"},{"id":"T68","span":{"begin":1581,"end":1651},"obj":"Sentence"},{"id":"T69","span":{"begin":1652,"end":1753},"obj":"Sentence"},{"id":"T70","span":{"begin":1754,"end":1832},"obj":"Sentence"},{"id":"T71","span":{"begin":1833,"end":1949},"obj":"Sentence"},{"id":"T72","span":{"begin":1950,"end":2007},"obj":"Sentence"},{"id":"T73","span":{"begin":2008,"end":2074},"obj":"Sentence"},{"id":"T74","span":{"begin":2075,"end":2180},"obj":"Sentence"},{"id":"T75","span":{"begin":2181,"end":2252},"obj":"Sentence"},{"id":"T76","span":{"begin":2253,"end":2325},"obj":"Sentence"},{"id":"T77","span":{"begin":2326,"end":2397},"obj":"Sentence"},{"id":"T78","span":{"begin":2398,"end":2452},"obj":"Sentence"}],"namespaces":[{"prefix":"_base","uri":"http://pubannotation.org/ontology/tao.owl#"}],"attributes":[{"subj":"T51","pred":"source","obj":"LitCovid-sentences"},{"subj":"T52","pred":"source","obj":"LitCovid-sentences"},{"subj":"T53","pred":"source","obj":"LitCovid-sentences"},{"subj":"T54","pred":"source","obj":"LitCovid-sentences"},{"subj":"T55","pred":"source","obj":"LitCovid-sentences"},{"subj":"T56","pred":"source","obj":"LitCovid-sentences"},{"subj":"T57","pred":"source","obj":"LitCovid-sentences"},{"subj":"T58","pred":"source","obj":"LitCovid-sentences"},{"subj":"T59","pred":"source","obj":"LitCovid-sentences"},{"subj":"T60","pred":"source","obj":"LitCovid-sentences"},{"subj":"T61","pred":"source","obj":"LitCovid-sentences"},{"subj":"T62","pred":"source","obj":"LitCovid-sentences"},{"subj":"T63","pred":"source","obj":"LitCovid-sentences"},{"subj":"T64","pred":"source","obj":"LitCovid-sentences"},{"subj":"T65","pred":"source","obj":"LitCovid-sentences"},{"subj":"T66","pred":"source","obj":"LitCovid-sentences"},{"subj":"T67","pred":"source","obj":"LitCovid-sentences"},{"subj":"T68","pred":"source","obj":"LitCovid-sentences"},{"subj":"T69","pred":"source","obj":"LitCovid-sentences"},{"subj":"T70","pred":"source","obj":"LitCovid-sentences"},{"subj":"T71","pred":"source","obj":"LitCovid-sentences"},{"subj":"T72","pred":"source","obj":"LitCovid-sentences"},{"subj":"T73","pred":"source","obj":"LitCovid-sentences"},{"subj":"T74","pred":"source","obj":"LitCovid-sentences"},{"subj":"T75","pred":"source","obj":"LitCovid-sentences"},{"subj":"T76","pred":"source","obj":"LitCovid-sentences"},{"subj":"T77","pred":"source","obj":"LitCovid-sentences"},{"subj":"T78","pred":"source","obj":"LitCovid-sentences"}]},{"project":"LitCovid-PubTator","denotations":[{"id":"104","span":{"begin":1629,"end":1637},"obj":"Disease"},{"id":"105","span":{"begin":1793,"end":1801},"obj":"Disease"},{"id":"106","span":{"begin":1876,"end":1884},"obj":"Disease"},{"id":"107","span":{"begin":1916,"end":1924},"obj":"Disease"},{"id":"108","span":{"begin":2148,"end":2156},"obj":"Disease"},{"id":"109","span":{"begin":2213,"end":2221},"obj":"Disease"},{"id":"110","span":{"begin":2286,"end":2294},"obj":"Disease"},{"id":"111","span":{"begin":2358,"end":2366},"obj":"Disease"}],"attributes":[{"id":"A104","pred":"tao:has_database_id","subj":"104","obj":"MESH:D007239"},{"id":"A105","pred":"tao:has_database_id","subj":"105","obj":"MESH:D007239"},{"id":"A106","pred":"tao:has_database_id","subj":"106","obj":"MESH:D007239"},{"id":"A107","pred":"tao:has_database_id","subj":"107","obj":"MESH:D007239"},{"id":"A108","pred":"tao:has_database_id","subj":"108","obj":"MESH:D007239"},{"id":"A109","pred":"tao:has_database_id","subj":"109","obj":"MESH:D007239"},{"id":"A110","pred":"tao:has_database_id","subj":"110","obj":"MESH:D007239"},{"id":"A111","pred":"tao:has_database_id","subj":"111","obj":"MESH:D007239"},{"subj":"104","pred":"source","obj":"LitCovid-PubTator"},{"subj":"105","pred":"source","obj":"LitCovid-PubTator"},{"subj":"106","pred":"source","obj":"LitCovid-PubTator"},{"subj":"107","pred":"source","obj":"LitCovid-PubTator"},{"subj":"108","pred":"source","obj":"LitCovid-PubTator"},{"subj":"109","pred":"source","obj":"LitCovid-PubTator"},{"subj":"110","pred":"source","obj":"LitCovid-PubTator"},{"subj":"111","pred":"source","obj":"LitCovid-PubTator"}],"namespaces":[{"prefix":"Tax","uri":"https://www.ncbi.nlm.nih.gov/taxonomy/"},{"prefix":"MESH","uri":"https://id.nlm.nih.gov/mesh/"},{"prefix":"Gene","uri":"https://www.ncbi.nlm.nih.gov/gene/"},{"prefix":"CVCL","uri":"https://web.expasy.org/cellosaurus/CVCL_"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"LitCovid-PD-MONDO","color":"#ec93ca","default":true},{"id":"LitCovid-PD-CLO","color":"#93e4ec"},{"id":"LitCovid-sentences","color":"#ecda93"},{"id":"LitCovid-PubTator","color":"#c093ec"}]}]}}