PMC:7047374 / 9193-13757 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/7047374","sourcedb":"PMC","sourceid":"7047374","source_url":"https://www.ncbi.nlm.nih.gov/pmc/7047374","text":"The simplified reservoir-people transmission network model\nWe assumed that the SARS-CoV-2 might be imported to the seafood market in a short time. Therefore, we added the further assumptions as follows: The transmission network of Bats-Host was ignored.\nBased on our previous studies on simulating importation [13, 14], we set the initial value of W as following impulse function: \\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}$$ Importation= impulse\\left(n,{t}_0,{t}_i\\right) $$\\end{document}Importation=impulsent0ti\nIn the function, n, t0 and ti refer to imported volume of the SARS-CoV-2 to the market, start time of the simulation, and the interval of the importation.\nTherefore, the BHRP model was simplified as RP model and is shown as follows: \\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}$$ \\left\\{\\kern0.5em \\begin{array}{c}\\frac{d{S}_P}{dt}={\\varLambda}_P-{m}_P{S}_P-{\\beta}_P{S}_P\\left({I}_P+\\upkappa {A}_P\\right)-{\\beta}_W{S}_PW\\kern11em \\\\ {}\\frac{d{E}_P}{dt}={\\beta}_P{S}_P\\left({I}_P+\\upkappa {A}_P\\right)+{\\beta}_W{S}_PW-\\left(1-{\\delta}_P\\right){\\upomega}_P{E}_P-{\\delta}_P{\\upomega}_P^{\\prime }{E}_P-{m}_P{E}_P\\kern0.5em \\\\ {}\\frac{d{I}_P}{dt}=\\left(1-{\\delta}_P\\right){\\upomega}_P{E}_P-\\left({\\gamma}_P+{m}_P\\right){I}_P\\kern16.5em \\\\ {}\\frac{d{A}_P}{dt}={\\delta}_P{\\upomega}_P^{\\prime }{E}_P-\\left({\\gamma}_P^{\\prime }+{m}_P\\right){A}_P\\kern18.75em \\\\ {}\\frac{d{R}_P}{dt}={\\gamma}_P{I}_P+{\\gamma}_P^{\\prime }{A}_P-{m}_P{R}_P\\kern20em \\\\ {}\\frac{dW}{dt}={\\mu}_P{I}_P+{\\mu}_P^{\\prime }{A}_P-\\varepsilon W\\kern20.5em \\end{array}\\right. $$\\end{document}dSPdt=ΛP−mPSP−βPSPIP+κAP−βWSPWdEPdt=βPSPIP+κAP+βWSPW−1−δPωPEP−δPωP′EP−mPEPdIPdt=1−δPωPEP−γP+mPIPdAPdt=δPωP′EP−γP′+mPAPdRPdt=γPIP+γP′AP−mPRPdWdt=μPIP+μP′AP−εW\nDuring the outbreak period, the natural birth rate and death rate in the population was in a relative low level. However, people would commonly travel into and out from Wuhan City mainly due to the Chinese New Year holiday. Therefore, nP and mP refer to the rate of people traveling into Wuhan City and traveling out from Wuhan City, respectively.\nIn the model, people and viruses have different dimensions. Based on our previous research [15], we therefore used the following sets to perform the normalization: \\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}$$ {s}_P=\\frac{S_P}{N_P},{e}_P=\\frac{E_P}{N_P},{i}_P=\\frac{I_P}{N_P}, {a}_P=\\frac{A_P}{N_P},{r}_P=\\frac{R_P}{N_P},w=\\frac{\\varepsilon W}{\\mu_P{N}_P},\\kern0.5em {\\mu}_P^{\\prime }=c{\\mu}_P,\\kern0.5em {b}_P={\\beta}_P{N}_P,\\mathrm{and}\\ {b}_W=\\frac{\\mu_P{\\beta}_W{N}_P}{\\varepsilon .} $$\\end{document}sP=SPNP,eP=EPNP,iP=IPNP,aP=APNP,rP=RPNP,w=εWμPNP,μP′=cμP,bP=βPNP,andbW=μPβWNPε.\nIn the normalization, parameter c refers to the relative shedding coefficient of AP compared to IP. The normalized RP model is changed as follows: \\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}$$ \\left\\{\\begin{array}{c}\\frac{d{s}_P}{dt}={n}_P-{m}_P{s}_P-{b}_P{s}_P\\left({i}_P+\\upkappa {a}_P\\right)-{b}_W{s}_Pw\\\\ {}\\frac{d{e}_P}{dt}={b}_P{s}_P\\left({i}_P+\\upkappa {a}_P\\right)+{b}_W{s}_Pw-\\left(1-{\\delta}_P\\right){\\upomega}_P{e}_P-{\\delta}_P{\\upomega}_P^{\\prime }{e}_P-{m}_P{e}_P\\\\ {}\\frac{d{i}_P}{dt}=\\left(1-{\\delta}_P\\right){\\upomega}_P{e}_P-\\left({\\gamma}_P+{m}_P\\right){i}_P\\\\ {}\\frac{d{a}_P}{dt}={\\delta}_P{\\upomega}_P^{\\prime }{e}_P-\\left({\\gamma}_P^{\\prime }+{m}_P\\right){a}_P\\kern26.5em \\\\ {}\\frac{d{r}_P}{dt}={\\gamma}_P{i}_P+{\\gamma}_P^{\\prime }{a}_P-{m}_P{r}_P\\\\ {}\\frac{dw}{dt}=\\varepsilon \\left({i}_P+c{a}_P-w\\right)\\kern28.2em \\end{array}\\right. 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