PMC:7047374 / 20510-22171 JSONTXT

{"project":"LitCovid-PD-FMA-UBERON","denotations":[{"id":"T11","span":{"begin":372,"end":378},"obj":"Body_part"},{"id":"T13","span":{"begin":945,"end":951},"obj":"Body_part"}],"attributes":[{"id":"A11","pred":"fma_id","subj":"T11","obj":"http://purl.org/sig/ont/fma/fma13444"},{"id":"A12","pred":"fma_id","subj":"T11","obj":"http://purl.org/sig/ont/fma/fma68614"},{"id":"A13","pred":"fma_id","subj":"T13","obj":"http://purl.org/sig/ont/fma/fma13444"},{"id":"A14","pred":"fma_id","subj":"T13","obj":"http://purl.org/sig/ont/fma/fma68614"}],"text":"By the next generation matrix approach, we can get the next generation matrix and R0 for the RP model: \\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}$$ F{V}^{-1}=\\left[\\begin{array}{cccc}{\\beta}_p\\frac{\\varLambda_P}{m_P}A+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}+{\\beta}_W\\frac{\\varLambda_P}{m_P}D\u0026 \\ast \u0026 \\ast \u0026 \\ast \\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\end{array}\\right] $$\\end{document}FV−1=βpΛPmPA+βPκΛPmP+βWΛPmPD∗∗∗000000000000\\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}$$ {R}_0=\\rho \\left(F{V}^{-1}\\right)={\\beta}_P\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right){\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)}+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}\\frac{\\delta_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)}+{\\beta}_W\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right)\\mu {\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)\\varepsilon }+\\beta W\\frac{\\varLambda_P}{m_P}\\frac{\\mu^{\\hbox{'}}{\\delta}_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)\\varepsilon } $$\\end{document}R0=ρFV−1=βPΛPmP1−δPωPωP+mPγP+mP+βPκΛPmPδPωPωP+mPγP'+mP+βWΛPmP1−δPμωPωP+mPγP+mPε+βWΛPmPμ'δPωPωP+mPγP'+mPε"}

{"project":"LitCovid-PD-CLO","denotations":[{"id":"T159","span":{"begin":438,"end":439},"obj":"http://purl.obolibrary.org/obo/CLO_0001020"},{"id":"T160","span":{"begin":933,"end":936},"obj":"http://purl.obolibrary.org/obo/CLO_0051142"}],"text":"By the next generation matrix approach, we can get the next generation matrix and R0 for the RP model: \\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}$$ F{V}^{-1}=\\left[\\begin{array}{cccc}{\\beta}_p\\frac{\\varLambda_P}{m_P}A+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}+{\\beta}_W\\frac{\\varLambda_P}{m_P}D\u0026 \\ast \u0026 \\ast \u0026 \\ast \\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\end{array}\\right] $$\\end{document}FV−1=βpΛPmPA+βPκΛPmP+βWΛPmPD∗∗∗000000000000\\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}$$ {R}_0=\\rho \\left(F{V}^{-1}\\right)={\\beta}_P\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right){\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)}+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}\\frac{\\delta_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)}+{\\beta}_W\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right)\\mu {\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)\\varepsilon }+\\beta W\\frac{\\varLambda_P}{m_P}\\frac{\\mu^{\\hbox{'}}{\\delta}_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)\\varepsilon } $$\\end{document}R0=ρFV−1=βPΛPmP1−δPωPωP+mPγP+mP+βPκΛPmPδPωPωP+mPγP'+mP+βWΛPmP1−δPμωPωP+mPγP+mPε+βWΛPmPμ'δPωPωP+mPγP'+mPε"}

{"project":"LitCovid-PD-CHEBI","denotations":[{"id":"T126","span":{"begin":93,"end":95},"obj":"Chemical"},{"id":"T127","span":{"begin":407,"end":411},"obj":"Chemical"},{"id":"T128","span":{"begin":442,"end":446},"obj":"Chemical"},{"id":"T129","span":{"begin":483,"end":487},"obj":"Chemical"},{"id":"T130","span":{"begin":616,"end":618},"obj":"Chemical"},{"id":"T131","span":{"begin":962,"end":966},"obj":"Chemical"},{"id":"T132","span":{"begin":1073,"end":1078},"obj":"Chemical"},{"id":"T133","span":{"begin":1098,"end":1102},"obj":"Chemical"},{"id":"T134","span":{"begin":1199,"end":1204},"obj":"Chemical"},{"id":"T135","span":{"begin":1235,"end":1239},"obj":"Chemical"},{"id":"T136","span":{"begin":1350,"end":1355},"obj":"Chemical"},{"id":"T137","span":{"begin":1386,"end":1390},"obj":"Chemical"},{"id":"T138","span":{"begin":1495,"end":1500},"obj":"Chemical"},{"id":"T139","span":{"begin":1561,"end":1563},"obj":"Chemical"}],"attributes":[{"id":"A126","pred":"chebi_id","subj":"T126","obj":"http://purl.obolibrary.org/obo/CHEBI_141419"},{"id":"A127","pred":"chebi_id","subj":"T127","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A128","pred":"chebi_id","subj":"T128","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A129","pred":"chebi_id","subj":"T129","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A130","pred":"chebi_id","subj":"T130","obj":"http://purl.obolibrary.org/obo/CHEBI_73638"},{"id":"A131","pred":"chebi_id","subj":"T131","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A132","pred":"chebi_id","subj":"T132","obj":"http://purl.obolibrary.org/obo/CHEBI_30212"},{"id":"A133","pred":"chebi_id","subj":"T133","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A134","pred":"chebi_id","subj":"T134","obj":"http://purl.obolibrary.org/obo/CHEBI_30212"},{"id":"A135","pred":"chebi_id","subj":"T135","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A136","pred":"chebi_id","subj":"T136","obj":"http://purl.obolibrary.org/obo/CHEBI_30212"},{"id":"A137","pred":"chebi_id","subj":"T137","obj":"http://purl.obolibrary.org/obo/CHEBI_10545"},{"id":"A138","pred":"chebi_id","subj":"T138","obj":"http://purl.obolibrary.org/obo/CHEBI_30212"},{"id":"A139","pred":"chebi_id","subj":"T139","obj":"http://purl.obolibrary.org/obo/CHEBI_73638"}],"text":"By the next generation matrix approach, we can get the next generation matrix and R0 for the RP model: \\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}$$ F{V}^{-1}=\\left[\\begin{array}{cccc}{\\beta}_p\\frac{\\varLambda_P}{m_P}A+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}+{\\beta}_W\\frac{\\varLambda_P}{m_P}D\u0026 \\ast \u0026 \\ast \u0026 \\ast \\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\end{array}\\right] $$\\end{document}FV−1=βpΛPmPA+βPκΛPmP+βWΛPmPD∗∗∗000000000000\\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}$$ {R}_0=\\rho \\left(F{V}^{-1}\\right)={\\beta}_P\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right){\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)}+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}\\frac{\\delta_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)}+{\\beta}_W\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right)\\mu {\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)\\varepsilon }+\\beta W\\frac{\\varLambda_P}{m_P}\\frac{\\mu^{\\hbox{'}}{\\delta}_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)\\varepsilon } $$\\end{document}R0=ρFV−1=βPΛPmP1−δPωPωP+mPγP+mP+βPκΛPmPδPωPωP+mPγP'+mP+βWΛPmP1−δPμωPωP+mPγP+mPε+βWΛPmPμ'δPωPωP+mPγP'+mPε"}

{"project":"LitCovid-sentences","denotations":[{"id":"T150","span":{"begin":0,"end":1661},"obj":"Sentence"}],"namespaces":[{"prefix":"_base","uri":"http://pubannotation.org/ontology/tao.owl#"}],"text":"By the next generation matrix approach, we can get the next generation matrix and R0 for the RP model: \\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}$$ F{V}^{-1}=\\left[\\begin{array}{cccc}{\\beta}_p\\frac{\\varLambda_P}{m_P}A+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}+{\\beta}_W\\frac{\\varLambda_P}{m_P}D\u0026 \\ast \u0026 \\ast \u0026 \\ast \\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\\\ {}0\u0026 0\u0026 0\u0026 0\\end{array}\\right] $$\\end{document}FV−1=βpΛPmPA+βPκΛPmP+βWΛPmPD∗∗∗000000000000\\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}$$ {R}_0=\\rho \\left(F{V}^{-1}\\right)={\\beta}_P\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right){\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)}+{\\beta}_P\\kappa \\frac{\\varLambda_P}{m_P}\\frac{\\delta_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)}+{\\beta}_W\\frac{\\varLambda_P}{m_P}\\frac{\\left(1-{\\delta}_P\\right)\\mu {\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P+{m}_P\\right)\\varepsilon }+\\beta W\\frac{\\varLambda_P}{m_P}\\frac{\\mu^{\\hbox{'}}{\\delta}_P{\\omega}_P}{\\left({\\omega}_P+{m}_P\\right)\\left({\\gamma}_P^{\\hbox{'}}+{m}_P\\right)\\varepsilon } $$\\end{document}R0=ρFV−1=βPΛPmP1−δPωPωP+mPγP+mP+βPκΛPmPδPωPωP+mPγP'+mP+βWΛPmP1−δPμωPωP+mPγP+mPε+βWΛPmPμ'δPωPωP+mPγP'+mPε"}