PMC:7547104 / 23463-28402
Annnotations
{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7547104","sourcedb":"PMC","sourceid":"7547104","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7547104","text":"The full model equations describing the dynamics of susceptible (Si), infected (Ii), quarantined (Qi), hospitalized (Hi), recovered (Ri) and deceased (Di) are1 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\dot S_i = - \\rho _i\\beta \\frac{{S_iI_i}}{{N_i}},$$\\end{document}S˙i=−ρiβSiIiNi,2 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\dot I_i = \\rho _i\\beta \\frac{{S_iI_i}}{{N_i}} - \\alpha _iI_i - \\psi _iI_i - \\gamma I_i,$$\\end{document}I˙i=ρiβSiIiNi−αiIi−ψiIi−γIi,3 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\dot Q_i = \\alpha _iI_i - \\kappa _i^HQ_i - \\eta _i^QQ_i + \\kappa _i^QH_i$$\\end{document}Q˙i=αiIi−κiHQi−ηiQQi+κiQHi4 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\dot H_i = \\kappa _i^HQ_i + \\psi _iI_i - \\eta _i^HH_i - \\zeta _i\\,H_i - \\kappa _i^QH_i$$\\end{document}H˙i=κiHQi+ψiIi−ηiHHi−ζiHi−κiQHi5 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\dot D_i = \\zeta _i\\,H_i,$$\\end{document}D˙i=ζiHi,6 \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\dot R_i = \\gamma I_i + \\eta _i^QQ_i + \\eta _i^HH_i$$\\end{document}R˙i=γIi+ηiQQi+ηiHHiwhere β and γ are the infection and recovery rate, respectively, which are assumed to be the same for all regions as COVID-19 is transmitted from person to person and there is no parasite vector or evidence of environmental parameters significantly altering its infection rate, ρi ∈[0, 1] is a parameter modelling the effects of social distancing measures in the i-th region, αi is the rate of infected that are detected and quarantined, ψi is the rate of infected that needs to be hospitalized, \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\eta _i^Q$$\\end{document}ηiQ is the rate of quarantined who recover, \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\eta _i^H$$\\end{document}ηiH is the fraction of hospitalized who recover, \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\kappa _i^Q$$\\end{document}κiQ is the rate of hospitalized that is transferred to home isolation, \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$\\kappa _i^H$$\\end{document}κiH is the rate of quarantined who need to be hospitalized, and ζi is the mortality rate that was shown from data analysis (see Supplementary Notes) to be a function of the ratio between Hi and the maximum number, say \\documentclass[12pt]{minimal} \t\t\t\t\\usepackage{amsmath} \t\t\t\t\\usepackage{wasysym} \t\t\t\t\\usepackage{amsfonts} \t\t\t\t\\usepackage{amssymb} \t\t\t\t\\usepackage{amsbsy} \t\t\t\t\\usepackage{mathrsfs} \t\t\t\t\\usepackage{upgreek} \t\t\t\t\\setlength{\\oddsidemargin}{-69pt} \t\t\t\t\\begin{document}$$T_i^H$$\\end{document}TiH, of patients that can be treated in ICU at the hospitals in i-th region. Ni is the actual population in region i, i.e., the resident population without those removed because they had been quarantined, hospitalized, deceased or had recovered.","divisions":[{"label":"label","span":{"begin":158,"end":159}},{"label":"label","span":{"begin":506,"end":507}},{"label":"label","span":{"begin":906,"end":907}},{"label":"label","span":{"begin":1288,"end":1289}},{"label":"label","span":{"begin":1689,"end":1690}},{"label":"label","span":{"begin":2007,"end":2008}}],"tracks":[{"project":"LitCovid-PD-MONDO","denotations":[{"id":"T11","span":{"begin":2383,"end":2392},"obj":"Disease"},{"id":"T12","span":{"begin":2478,"end":2486},"obj":"Disease"},{"id":"T13","span":{"begin":2623,"end":2632},"obj":"Disease"}],"attributes":[{"id":"A11","pred":"mondo_id","subj":"T11","obj":"http://purl.obolibrary.org/obo/MONDO_0005550"},{"id":"A12","pred":"mondo_id","subj":"T12","obj":"http://purl.obolibrary.org/obo/MONDO_0100096"},{"id":"A13","pred":"mondo_id","subj":"T13","obj":"http://purl.obolibrary.org/obo/MONDO_0005550"},{"subj":"T11","pred":"source","obj":"LitCovid-PD-MONDO"},{"subj":"T12","pred":"source","obj":"LitCovid-PD-MONDO"},{"subj":"T13","pred":"source","obj":"LitCovid-PD-MONDO"}]},{"project":"LitCovid-PD-CLO","denotations":[{"id":"T85","span":{"begin":440,"end":443},"obj":"http://purl.obolibrary.org/obo/CLO_0051142"},{"id":"T86","span":{"begin":786,"end":789},"obj":"http://purl.obolibrary.org/obo/CLO_0051142"},{"id":"T87","span":{"begin":2653,"end":2654},"obj":"http://purl.obolibrary.org/obo/CLO_0001020"},{"id":"T88","span":{"begin":4344,"end":4345},"obj":"http://purl.obolibrary.org/obo/CLO_0001020"}],"attributes":[{"subj":"T85","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T86","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T87","pred":"source","obj":"LitCovid-PD-CLO"},{"subj":"T88","pred":"source","obj":"LitCovid-PD-CLO"}]},{"project":"LitCovid-PD-CHEBI","denotations":[{"id":"T13","span":{"begin":65,"end":67},"obj":"Chemical"},{"id":"T14","span":{"begin":447,"end":451},"obj":"Chemical"},{"id":"T15","span":{"begin":793,"end":797},"obj":"Chemical"},{"id":"T16","span":{"begin":824,"end":829},"obj":"Chemical"},{"id":"T17","span":{"begin":852,"end":857},"obj":"Chemical"},{"id":"T18","span":{"begin":1186,"end":1191},"obj":"Chemical"},{"id":"T19","span":{"begin":2287,"end":2292},"obj":"Chemical"},{"id":"T20","span":{"begin":4771,"end":4773},"obj":"Chemical"}],"attributes":[{"id":"A13","pred":"chebi_id","subj":"T13","obj":"http://purl.obolibrary.org/obo/CHEBI_27573"},{"id":"A14","pred":"chebi_id","subj":"T14","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A15","pred":"chebi_id","subj":"T15","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A16","pred":"chebi_id","subj":"T16","obj":"http://purl.obolibrary.org/obo/CHEBI_30216"},{"id":"A17","pred":"chebi_id","subj":"T17","obj":"http://purl.obolibrary.org/obo/CHEBI_30212"},{"id":"A18","pred":"chebi_id","subj":"T18","obj":"http://purl.obolibrary.org/obo/CHEBI_30216"},{"id":"A19","pred":"chebi_id","subj":"T19","obj":"http://purl.obolibrary.org/obo/CHEBI_30212"},{"id":"A20","pred":"chebi_id","subj":"T20","obj":"http://purl.obolibrary.org/obo/CHEBI_28112"},{"subj":"T13","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T14","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T15","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T16","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T17","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T18","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T19","pred":"source","obj":"LitCovid-PD-CHEBI"},{"subj":"T20","pred":"source","obj":"LitCovid-PD-CHEBI"}]},{"project":"LitCovid-sentences","denotations":[{"id":"T131","span":{"begin":0,"end":4770},"obj":"Sentence"},{"id":"T132","span":{"begin":4771,"end":4939},"obj":"Sentence"}],"namespaces":[{"prefix":"_base","uri":"http://pubannotation.org/ontology/tao.owl#"}],"attributes":[{"subj":"T131","pred":"source","obj":"LitCovid-sentences"},{"subj":"T132","pred":"source","obj":"LitCovid-sentences"}]},{"project":"LitCovid-PubTator","denotations":[{"id":"76","span":{"begin":4702,"end":4710},"obj":"Species"},{"id":"77","span":{"begin":70,"end":78},"obj":"Disease"},{"id":"78","span":{"begin":2383,"end":2392},"obj":"Disease"},{"id":"79","span":{"begin":2478,"end":2486},"obj":"Disease"},{"id":"80","span":{"begin":2623,"end":2632},"obj":"Disease"},{"id":"81","span":{"begin":2755,"end":2763},"obj":"Disease"},{"id":"82","span":{"begin":2817,"end":2825},"obj":"Disease"},{"id":"83","span":{"begin":4263,"end":4272},"obj":"Disease"}],"attributes":[{"id":"A76","pred":"tao:has_database_id","subj":"76","obj":"Tax:9606"},{"id":"A77","pred":"tao:has_database_id","subj":"77","obj":"MESH:D007239"},{"id":"A78","pred":"tao:has_database_id","subj":"78","obj":"MESH:D007239"},{"id":"A79","pred":"tao:has_database_id","subj":"79","obj":"MESH:C000657245"},{"id":"A80","pred":"tao:has_database_id","subj":"80","obj":"MESH:D007239"},{"id":"A81","pred":"tao:has_database_id","subj":"81","obj":"MESH:D007239"},{"id":"A82","pred":"tao:has_database_id","subj":"82","obj":"MESH:D007239"},{"id":"A83","pred":"tao:has_database_id","subj":"83","obj":"MESH:D003643"},{"subj":"76","pred":"source","obj":"LitCovid-PubTator"},{"subj":"77","pred":"source","obj":"LitCovid-PubTator"},{"subj":"78","pred":"source","obj":"LitCovid-PubTator"},{"subj":"79","pred":"source","obj":"LitCovid-PubTator"},{"subj":"80","pred":"source","obj":"LitCovid-PubTator"},{"subj":"81","pred":"source","obj":"LitCovid-PubTator"},{"subj":"82","pred":"source","obj":"LitCovid-PubTator"},{"subj":"83","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":"#ec93e3","default":true},{"id":"LitCovid-PD-CLO","color":"#93ecdb"},{"id":"LitCovid-PD-CHEBI","color":"#ecc093"},{"id":"LitCovid-sentences","color":"#a693ec"},{"id":"LitCovid-PubTator","color":"#99ec93"}]}]}}