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Id Subject Object Predicate Lexical cue
T1 0-91 Sentence denotes A mathematical model for simulating the phase-based transmissibility of a novel coronavirus
T2 93-101 Sentence denotes Abstract
T3 102-112 Sentence denotes Background
T4 113-310 Sentence denotes As reported by the World Health Organization, a novel coronavirus (2019-nCoV) was identified as the causative virus of Wuhan pneumonia of unknown etiology by Chinese authorities on 7 January, 2020.
T5 311-466 Sentence denotes The virus was named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by International Committee on Taxonomy of Viruses on 11 February, 2020.
T6 467-566 Sentence denotes This study aimed to develop a mathematical model for calculating the transmissibility of the virus.
T7 568-575 Sentence denotes Methods
T8 576-771 Sentence denotes In this study, we developed a Bats-Hosts-Reservoir-People transmission network model for simulating the potential transmission from the infection source (probably be bats) to the human infection.
T9 772-1029 Sentence denotes Since the Bats-Hosts-Reservoir network was hard to explore clearly and public concerns were focusing on the transmission from Huanan Seafood Wholesale Market (reservoir) to people, we simplified the model as Reservoir-People (RP) transmission network model.
T10 1030-1193 Sentence denotes The next generation matrix approach was adopted to calculate the basic reproduction number (R0) from the RP model to assess the transmissibility of the SARS-CoV-2.
T11 1195-1202 Sentence denotes Results
T12 1203-1466 Sentence denotes The value of R0 was estimated of 2.30 from reservoir to person and 3.58 from person to person which means that the expected number of secondary infections that result from introducing a single infected individual into an otherwise susceptible population was 3.58.
T13 1468-1479 Sentence denotes Conclusions
T14 1480-1711 Sentence denotes Our model showed that the transmissibility of SARS-CoV-2 was higher than the Middle East respiratory syndrome in the Middle East countries, similar to severe acute respiratory syndrome, but lower than MERS in the Republic of Korea.
T15 1713-1723 Sentence denotes Background
T16 1724-2207 Sentence denotes On 31 December 2019, the World Health Organization (WHO) China Country Office was informed of cases of pneumonia of unknown etiology (unknown cause) detected in Wuhan City, Hubei Province of China, and WHO reported that a novel coronavirus (2019-nCoV), which was named as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) by International Committee on Taxonomy of Viruses on 11 February, 2020, was identified as the causative virus by Chinese authorities on 7 January [1].
T17 2208-2381 Sentence denotes It is reported that the virus might be bat origin [2], and the transmission of the virus might related to a seafood market (Huanan Seafood Wholesale Market) exposure [3, 4].
T18 2382-2481 Sentence denotes The genetic features and some clinical findings of the infection have been reported recently [4–6].
T19 2482-2566 Sentence denotes Potentials for international spread via commercial air travel had been assessed [7].
T20 2567-2660 Sentence denotes Public health concerns are being paid globally on how many people are infected and suspected.
T21 2661-2795 Sentence denotes Therefore, it is urgent to develop a mathematical model to estimate the transmissibility and dynamic of the transmission of the virus.
T22 2796-2868 Sentence denotes There were several researches focusing on mathematical modelling [3, 8].
T23 2869-3094 Sentence denotes These researches focused on calculating the basic reproduction number (R0) by using the serial intervals and intrinsic growth rate [3, 9, 10], or using ordinary differential equations and Markov Chain Monte Carlo methods [8].
T24 3095-3224 Sentence denotes However, the bat origin and the transmission route form the seafood market to people were not considered in the published models.
T25 3225-3427 Sentence denotes In this study, we developed a Bats-Hosts-Reservoir-People (BHRP) transmission network model for simulating the potential transmission from the infection source (probably be bats) to the human infection.
T26 3428-3779 Sentence denotes Since the Bats-Hosts-Reservoir network was hard to explore clearly and public concerns were focusing on the transmission from Huanan Seafood Wholesale Market (reservoir) to people, we simplified the model as Reservoir-People (RP) transmission network model, and R0 was calculated based on the RP model to assess the transmissibility of the SARS-CoV-2.
T27 3781-3788 Sentence denotes Methods
T28 3790-3801 Sentence denotes Data source
T29 3802-3942 Sentence denotes The reported cases of SARS-CoV-2, which have been named as COVID-19, were collected for the modelling study from a published literature [3].
T30 3943-4089 Sentence denotes As reported by Li et al. [3], the onset date of the first case was on 7 December, 2020, and the seafood market was closed on 1 January, 2020 [11].
T31 4090-4218 Sentence denotes The epidemic curve from 7 December, 2019 to 1 January, 2020 was collected for our study, and the simulation time step was 1 day.
T32 4220-4263 Sentence denotes Simulation methods and statistical analysis
T33 4264-4376 Sentence denotes Berkeley Madonna 8.3.18 (developed by Robert Macey and George Oster of the University of California at Berkeley.
T34 4377-4406 Sentence denotes Copyright©1993–2001 Robert I.
T35 4407-4424 Sentence denotes Macey & George F.
T36 4425-4467 Sentence denotes Oster) was employed for the curve fitting.
T37 4468-4568 Sentence denotes The fourth-order Runge–Kutta method, with tolerance set at 0.001, was used to perform curve fitting.
T38 4569-4703 Sentence denotes While the curve fitting is in progress, Berkeley Madonna displays the root mean square deviation between the data and best run so far.
T39 4704-4785 Sentence denotes The coefficient of determination (R2) was employed to assess the goodness-of-fit.
T40 4786-4858 Sentence denotes SPSS 13.0 (IBM Corp., Armonk, NY, USA) was employed to calculate the R2.
T41 4860-4925 Sentence denotes The Bats-Hosts-Reservoir-People (BHRP) transmission network model
T42 4926-5009 Sentence denotes The BHRP transmission network model was posted to bioRxiv on 19 January, 2020 [12].
T43 5010-5131 Sentence denotes We assumed that the virus transmitted among the bats, and then transmitted to unknown hosts (probably some wild animals).
T44 5132-5233 Sentence denotes The hosts were hunted and sent to the seafood market which was defined as the reservoir of the virus.
T45 5234-5303 Sentence denotes People exposed to the market got the risks of the infection (Fig. 1).
T46 5304-5388 Sentence denotes The BHRP transmission network model was based on the following assumptions or facts:
T47 5389-5519 Sentence denotes The bats were divided into four compartments: susceptible bats (SB), exposed bats (EB), infected bats (IB), and removed bats (RB).
T48 5520-5584 Sentence denotes The birth rate and death rate of bats were defined as nB and mB.
T49 5585-5697 Sentence denotes In this model, we set ɅB = nB × NB as the number of the newborn bats where NB refer to the total number of bats.
T50 5698-5820 Sentence denotes The incubation period of bat infection was defined as 1/ωB and the infectious period of bat infection was defined as 1/γB.
T51 5821-5925 Sentence denotes The SB will be infected through sufficient contact with IB, and the transmission rate was defined as βB.
T52 5926-6066 Sentence denotes The hosts were also divided into four compartments: susceptible hosts (SH), exposed hosts (EH), infected hosts (IH), and removed hosts (RH).
T53 6067-6132 Sentence denotes The birth rate and death rate of hosts were defined as nH and mH.
T54 6133-6212 Sentence denotes In this model, we set ɅH = nH × NH where NH refer to the total number of hosts.
T55 6213-6337 Sentence denotes The incubation period of host infection was defined as 1/ωH and the infectious period of host infection was defined as 1/γH.
T56 6338-6473 Sentence denotes The SH will be infected through sufficient contact with IB and IH, and the transmission rates were defined as βBH and βH, respectively.
T57 6474-6540 Sentence denotes The SARS-CoV-2 in reservoir (the seafood market) was denoted as W.
T58 6541-6801 Sentence denotes We assumed that the retail purchases rate of the hosts in the market was a, and that the prevalence of SARS-CoV-2 in the purchases was IH/NH, therefore, the rate of the SARS-CoV-2 in W imported form the hosts was aWIH/NH where NH was the total number of hosts.
T59 6802-7001 Sentence denotes We also assumed that symptomatic infected people and asymptomatic infected people could export the virus into W with the rate of μP and μ’P, although this assumption might occur in a low probability.
T60 7002-7115 Sentence denotes The virus in W will subsequently leave the W compartment at a rate of εW, where 1/ε is the lifetime of the virus.
T61 7116-7340 Sentence denotes The people were divided into five compartments: susceptible people (SP), exposed people (EP), symptomatic infected people (IP), asymptomatic infected people (AP), and removed people (RP) including recovered and death people.
T62 7341-7407 Sentence denotes The birth rate and death rate of people were defined as nP and mP.
T63 7408-7488 Sentence denotes In this model, we set ɅP = nP × NP where NP refer to the total number of people.
T64 7489-7578 Sentence denotes The incubation period and latent period of human infection was defined as 1/ωP and 1/ω’P.
T65 7579-7644 Sentence denotes The infectious period of IP and AP was defined as 1/γP and 1/γ’P.
T66 7645-7704 Sentence denotes The proportion of asymptomatic infection was defined as δP.
T67 7705-7838 Sentence denotes The SP will be infected through sufficient contact with W and IP, and the transmission rates were defined as βW and βP, respectively.
T68 7839-7927 Sentence denotes We also assumed that the transmissibility of AP was κ times that of IP, where 0 ≤ κ ≤ 1.
T69 7928-8006 Sentence denotes Fig. 1 Flowchart of the Bats-Hosts-Reservoir-People transmission network model
T70 8007-8062 Sentence denotes The parameters of the BHRP model were shown in Table 1.
T71 8063-8149 Sentence denotes Table 1 Definition of those parameters in the Bats-Hosts-Reservoir-People (BHRP) model
T72 8150-8171 Sentence denotes Parameter Description
T73 8172-8207 Sentence denotes nB The birth rate parameter of bats
T74 8208-8244 Sentence denotes nH The birth rate parameter of hosts
T75 8245-8282 Sentence denotes nP The birth rate parameter of people
T76 8283-8308 Sentence denotes mB The death rate of bats
T77 8309-8335 Sentence denotes mH The death rate of hosts
T78 8336-8363 Sentence denotes mP The death rate of people
T79 8364-8398 Sentence denotes 1/ωB The incubation period of bats
T80 8399-8434 Sentence denotes 1/ωH The incubation period of hosts
T81 8435-8471 Sentence denotes 1/ωP The incubation period of people
T82 8472-8505 Sentence denotes 1/ω’P The latent period of people
T83 8506-8540 Sentence denotes 1/γB The infectious period of bats
T84 8541-8576 Sentence denotes 1/γH The infectious period of hosts
T85 8577-8638 Sentence denotes 1/γP The infectious period of symptomatic infection of people
T86 8639-8702 Sentence denotes 1/γ’P The infectious period of asymptomatic infection of people
T87 8703-8741 Sentence denotes βB The transmission rate from IB to SB
T88 8742-8781 Sentence denotes βBH The transmission rate from IB to SH
T89 8782-8820 Sentence denotes βH The transmission rate from IH to SH
T90 8821-8859 Sentence denotes βP The transmission rate from IP to SP
T91 8860-8897 Sentence denotes βW The transmission rate from W to SP
T92 8898-8952 Sentence denotes a The retail purchases rate of the hosts in the market
T93 8953-8994 Sentence denotes μP The shedding coefficients from IP to W
T94 8995-9037 Sentence denotes μ’P The shedding coefficients from AP to W
T95 9038-9072 Sentence denotes 1/ε The lifetime of the virus in W
T96 9073-9131 Sentence denotes δP The proportion of asymptomatic infection rate of people
T97 9132-9191 Sentence denotes κ The multiple of the transmissibility of AP to that of IP.
T98 9193-9251 Sentence denotes The simplified reservoir-people transmission network model
T99 9252-9339 Sentence denotes We assumed that the SARS-CoV-2 might be imported to the seafood market in a short time.
T100 9340-9395 Sentence denotes Therefore, we added the further assumptions as follows:
T101 9396-9446 Sentence denotes The transmission network of Bats-Host was ignored.
T102 9447-9928 Sentence denotes Based on our previous studies on simulating importation [13, 14], we set the initial value of W as following impulse function: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ Importation= impulse\left(n,{t}_0,{t}_i\right) $$\end{document}Importation=impulsent0ti
T103 9929-10083 Sentence denotes In 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.
T104 10084-11356 Sentence denotes Therefore, the BHRP model was simplified as RP model and is shown as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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
T105 11357-11469 Sentence denotes During the outbreak period, the natural birth rate and death rate in the population was in a relative low level.
T106 11470-11580 Sentence denotes However, people would commonly travel into and out from Wuhan City mainly due to the Chinese New Year holiday.
T107 11581-11704 Sentence denotes Therefore, nP and mP refer to the rate of people traveling into Wuhan City and traveling out from Wuhan City, respectively.
T108 11705-11764 Sentence denotes In the model, people and viruses have different dimensions.
T109 11765-12509 Sentence denotes Based on our previous research [15], we therefore used the following sets to perform the normalization: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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.
T110 12510-12609 Sentence denotes In the normalization, parameter c refers to the relative shedding coefficient of AP compared to IP.
T111 12610-13757 Sentence denotes The normalized RP model is changed as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\{\begin{array}{c}\frac{d{s}_P}{dt}={n}_P-{m}_P{s}_P-{b}_P{s}_P\left({i}_P+\upkappa {a}_P\right)-{b}_W{s}_Pw\\ {}\frac{d{e}_P}{dt}={b}_P{s}_P\left({i}_P+\upkappa {a}_P\right)+{b}_W{s}_Pw-\left(1-{\delta}_P\right){\upomega}_P{e}_P-{\delta}_P{\upomega}_P^{\prime }{e}_P-{m}_P{e}_P\\ {}\frac{d{i}_P}{dt}=\left(1-{\delta}_P\right){\upomega}_P{e}_P-\left({\gamma}_P+{m}_P\right){i}_P\\ {}\frac{d{a}_P}{dt}={\delta}_P{\upomega}_P^{\prime }{e}_P-\left({\gamma}_P^{\prime }+{m}_P\right){a}_P\kern26.5em \\ {}\frac{d{r}_P}{dt}={\gamma}_P{i}_P+{\gamma}_P^{\prime }{a}_P-{m}_P{r}_P\\ {}\frac{dw}{dt}=\varepsilon \left({i}_P+c{a}_P-w\right)\kern28.2em \end{array}\right. $$\end{document}dsPdt=nP−mPsP−bPsPiP+κaP−bWsPwdePdt=bPsPiP+κaP+bWsPw−1−δPωPeP−δPωP′eP−mPePdiPdt=1−δPωPeP−γP+mPiPdaPdt=δPωP′eP−γP′+mPaPdrPdt=γPiP+γP′aP−mPrPdwdt=εiP+caP−w
T112 13759-13819 Sentence denotes The transmissibility of the SARS-CoV-2 based on the RP model
T113 13820-13899 Sentence denotes In this study, we used the R0 to assess the transmissibility of the SARS-CoV-2.
T114 13900-14084 Sentence denotes Commonly, R0 was defined as the expected number of secondary infections that result from introducing a single infected individual into an otherwise susceptible population [13, 16, 17].
T115 14085-14120 Sentence denotes If R0 > 1, the outbreak will occur.
T116 14121-14164 Sentence denotes If R0 < 1, the outbreak will toward an end.
T117 14165-14257 Sentence denotes In this study, R0 was deduced from the RP model by the next generation matrix approach [18].
T118 14259-14279 Sentence denotes Parameter estimation
T119 14280-14355 Sentence denotes The parameters were estimated based on the following facts and assumptions:
T120 14356-14426 Sentence denotes The mean incubation period was 5.2 days (95% confidence interval [CI]:
T121 14427-14440 Sentence denotes 4.1–7.0) [3].
T122 14441-14535 Sentence denotes We set the same value (5.2 days) of the incubation period and the latent period in this study.
T123 14536-14560 Sentence denotes Thus, ωP = ω’P = 0.1923.
T124 14561-14759 Sentence denotes There is a mean 5-day delay from symptom onset to detection/hospitalization of a case (the cases detected in Thailand and Japan were hospitalized from 3 to 7 days after onset, respectively) [19–21].
T125 14760-14920 Sentence denotes The duration from illness onset to first medical visit for the 45 patients with illness onset before January 1 was estimated to have a mean of 5.8 days (95% CI:
T126 14921-14934 Sentence denotes 4.3–7.5) [3].
T127 14935-15003 Sentence denotes In our model, we set the infectious period of the cases as 5.8 days.
T128 15004-15027 Sentence denotes Therefore, γP = 0.1724.
T129 15028-15174 Sentence denotes Since there was no data on the proportion of asymptomatic infection of the virus, we simulated the baseline value of proportion of 0.5 (δP = 0.5).
T130 15175-15421 Sentence denotes Since there was no evidence about the transmissibility of asymptomatic infection, we assumed that the transmissibility of asymptomatic infection was 0.5 times that of symptomatic infection (κ = 0.5), which was the similar value as influenza [22].
T131 15422-15494 Sentence denotes We assumed that the relative shedding rate of AP compared to IP was 0.5.
T132 15495-15509 Sentence denotes Thus, c = 0.5.
T133 15510-15703 Sentence denotes Since 14 January, 2020, Wuhan City has strengthened the body temperature detection of passengers leaving Wuhan at airports, railway stations, long-distance bus stations and passenger terminals.
T134 15704-15801 Sentence denotes As of January 17, a total of nearly 0.3 million people had been tested for body temperature [23].
T135 15802-15864 Sentence denotes In Wuhan, there are about 2.87 million mobile population [24].
T136 15865-16106 Sentence denotes We assumed that there was 0.1 million people moving out to Wuhan City per day since January 10, 2020, and we believe that this number would increase (mainly due to the winter vacation and the Chinese New Year holiday) until 24 January, 2020.
T137 16107-16188 Sentence denotes This means that the 2.87 million would move out from Wuhan City in about 14 days.
T138 16189-16261 Sentence denotes Therefore, we set the moving volume of 0.2 million per day in our model.
T139 16262-16419 Sentence denotes Since the population of Wuhan was about 11 million at the end of 2018 [25], the rate of people traveling out from Wuhan City would be 0.018 (0.2/11) per day.
T140 16420-16532 Sentence denotes However, we assumed that the normal population mobility before January 1 was 0.1 times as that after January 10.
T141 16533-16650 Sentence denotes Therefore, we set the rate of people moving into and moving out from Wuhan City as 0.0018 per day (nP = mP = 0.0018).
T142 16651-16736 Sentence denotes The parameters bP and bW were estimated by fitting the model with the collected data.
T143 16737-16844 Sentence denotes At the beginning of the simulation, we assumed that the prevalence of the virus in the market was 1/100000.
T144 16845-17036 Sentence denotes Since the SARS-CoV-2 is an RNA virus, we assumed that it could be died in the environment in a short time, but it could be stay for a longer time (10 days) in the unknown hosts in the market.
T145 17037-17052 Sentence denotes We set ε = 0.1.
T146 17054-17061 Sentence denotes Results
T147 17062-17194 Sentence denotes In this study, we assumed that the incubation period (1/ωP) was the same as latent period (1/ω’P) of human infection, thus ωP = ω’P.
T148 17195-18388 Sentence denotes Based on the equations of RP model, we can get the disease free equilibrium point as: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(\frac{\varLambda_P}{m_P},0,0,0,0,0\right) $$\end{document}ΛPmP00000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F=\left[\begin{array}{cccc}0& {\beta}_P\frac{\varLambda_P}{m_P}& {\beta}_P\kappa \frac{\varLambda_P}{m_P}& {\beta}_W\frac{\varLambda_P}{m_P}\\ {}0& 0& 0& 0\\ {}0& 0& 0& 0\\ {}0& 0& 0& 0\end{array}\right],{V}^{-1}=\left[\begin{array}{cccc}\frac{1}{\omega_P+{m}_P}& 0& 0& 0\\ {}A& \frac{1}{\gamma_P+{m}_P}& 0& 0\\ {}B& 0& \frac{1}{\gamma_P^{\hbox{'}}+{m}_P}& 0\\ {}B& E& G& \frac{1}{\varepsilon}\end{array}\right] $$\end{document}F=0βPΛPmPβPκΛPmPβWΛPmP000000000000,V−1=1ωP+mP000A1γP+mP00B01γP'+mP0BEG1ε
T149 18389-20509 Sentence denotes In the matrix: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ A=\frac{\left(1-{\delta}_P\right){\upomega}_P}{\left({\upomega}_P+{m}_P\right)\left({\gamma}_P+{m}_P\right)} $$\end{document}A=1−δPωPωP+mPγP+mP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ B=\frac{\delta_P{\upomega}_P}{\left({\upomega}_P+{m}_P\right)\left({\gamma}_p^{\prime }+{m}_P\right)} $$\end{document}B=δPωPωP+mPγp′+mP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ D=\frac{\left(1-{\delta}_P\right){\mu \upomega}_P}{\left({\upomega}_P+{m}_P\right)\left({\gamma}_P+{m}_P\right)\varepsilon }+\frac{\mu^{\prime }{\delta}_P{\upomega}_P}{\left({\upomega}_P+{m}_P\right)\left({\gamma}_p^{\prime }+{m}_P\right)\varepsilon } $$\end{document}D=1−δPμωPωP+mPγP+mPε+μ′δPωPωP+mPγp′+mPε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ E=\frac{\mu }{\left({\gamma}_P+{m}_P\right)\varepsilon } $$\end{document}E=μγP+mPε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ G=\frac{\mu^{\prime }}{\left({\gamma}_p^{\prime }+{m}_P\right)\varepsilon } $$\end{document}G=μ′γp′+mPε
T150 20510-22171 Sentence denotes By the next generation matrix approach, we can get the next generation matrix and R0 for the RP model: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F{V}^{-1}=\left[\begin{array}{cccc}{\beta}_p\frac{\varLambda_P}{m_P}A+{\beta}_P\kappa \frac{\varLambda_P}{m_P}+{\beta}_W\frac{\varLambda_P}{m_P}D& \ast & \ast & \ast \\ {}0& 0& 0& 0\\ {}0& 0& 0& 0\\ {}0& 0& 0& 0\end{array}\right] $$\end{document}FV−1=βpΛPmPA+βPκΛPmP+βWΛPmPD∗∗∗000000000000\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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
T151 22172-23390 Sentence denotes The R0 of the normalized RP model is shown as follows: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {R}_0={b}_p\frac{n_P}{m_p}\frac{\left(1-{\delta}_P\right){\omega}_P}{\left[\left(1-\delta p\right){\omega}_P+{\delta}_P{\omega}_P^{\hbox{'}}+{m}_P\right]\left({\gamma}_P+{m}_P\right)}+\kappa {b}_P\frac{n_P}{m_P}\frac{\delta_P{\omega}_P^{\hbox{'}}}{\left[\left(1-{\delta}_P\right){\omega}_P+{\delta}_P{\omega}_P^{\hbox{'}}+{m}_P\right]\left({\gamma}_P^{\hbox{'}}+{m}_P\right)}+{b}_W\frac{n_P}{m_P}\frac{\left(1-{\delta}_p\right){\omega}_p}{\left[\left(1-{\delta}_p\right){\omega}_P+{\delta}_P{\omega}_P^{\hbox{'}}+{m}_p\right]\left({\gamma}_P+{m}_P\right)}+{b}_W\frac{n_P}{m_P}\frac{c{\delta}_P{\omega}_P^{\hbox{'}}}{\left[\left(1-{\delta}_p\right){\omega}_P+{\delta}_P{\omega}_P^{\hbox{'}}+{m}_p\right]\left({\gamma}_P^{\hbox{'}}+{m}_P\right)} $$\end{document}R0=bpnPmp1−δPωP1−δpωP+δPωP'+mPγP+mP+κbPnPmPδPωP'1−δPωP+δPωP'+mPγP'+mP+bWnPmP1−δpωp1−δpωP+δPωP'+mpγP+mP+bWnPmPcδPωP'1−δpωP+δPωP'+mpγP'+mP
T152 23391-23532 Sentence denotes Our modelling results showed that the normalized RP model fitted well to the reported SARS-CoV-2 cases data (R2 = 0.512, P < 0.001) (Fig. 2).
T153 23533-23823 Sentence denotes The value of R0 was estimated of 2.30 from reservoir to person, and from person to person and 3.58 from person to person which means that the expected number of secondary infections that result from introducing a single infected individual into an otherwise susceptible population was 3.58.
T154 23824-23868 Sentence denotes Fig. 2 Curve fitting results of the RP model
T155 23870-23880 Sentence denotes Discussion
T156 23881-24039 Sentence denotes In this study, we developed RP transmission model, which considering the routes from reservoir to person and from person to person of SARS-CoV-2 respectively.
T157 24040-24135 Sentence denotes We used the models to fit the reported data in Wuhan City, China from published literature [3].
T158 24136-24223 Sentence denotes The simulation results showed that the R0 of SARS-CoV-2 was 3.58 from person to person.
T159 24224-24295 Sentence denotes There was a research showed that the R0 of SARS-CoV-2 was 2.68 (95% CI:
T160 24296-24311 Sentence denotes 2.47–2.86) [8].
T161 24312-24378 Sentence denotes Another research showed that the R0 of SARS-CoV-2 was 2.2 (95% CI:
T162 24379-24392 Sentence denotes 1.4–3.9) [3].
T163 24393-24452 Sentence denotes The different values might be due to the different methods.
T164 24453-24579 Sentence denotes The methods which Li et al. employed were based on the epidemic growth rate of the epidemic curve and the serial interval [3].
T165 24580-24808 Sentence denotes Our previous study showed that several methods could be used to calculate the R0 based on the epidemic growth rate of the epidemic curve and the serial interval, and different methods might result in different values of R0 [26].
T166 24809-24939 Sentence denotes Our results also showed that the R0 of SARS-CoV-2 was 2.30 from reservoir to person which was lower than that of person to person.
T167 24940-25102 Sentence denotes This means that the transmission route was mainly from person to person rather than from reservoir to person in the early stage of the transmission in Wuhan City.
T168 25103-25263 Sentence denotes However, this result was based on the limited data from a published literature, and it might not show the real situation at the early stage of the transmission.
T169 25264-25392 Sentence denotes Researches showed that the R0 of severe acute respiratory syndrome (SARS) was about 2.7–3.4 or 2–4 in Hong Kong, China [27, 28].
T170 25393-25520 Sentence denotes Another research found that the R0 of SARS was about 2.1 in Hong Kong, China, 2.7 in Singapore, and 3.8 in Beijing, China [29].
T171 25521-25622 Sentence denotes Therefore, we believe that the commonly acceptable average value of the R0 of SARS might be 2.9 [30].
T172 25623-25715 Sentence denotes The transmissibility of the Middle East respiratory syndrome (MERS) is much lower than SARS.
T173 25716-25881 Sentence denotes The reported value of the R0 of MERS was about 0.8–1.3 [31], with the inter-human transmissibility of the disease was about 0.6 or 0.9 in Middle East countries [32].
T174 25882-25997 Sentence denotes However, MERS had a high transmissibility in the outbreak in the Republic of Korea with the R0 of 2.5–7.2 [33, 34].
T175 25998-26174 Sentence denotes Therefore, the transmissibility of SARS-CoV-2 might be higher than MERS in the Middle East countries, similar to SARS, but lower than MERS transmitted in the Republic of Korea.
T176 26175-26248 Sentence denotes To contain the transmission of the virus, it is important to decrease R0.
T177 26249-26352 Sentence denotes According to the equation of R0 deduced from the simplified RP model, R0 is related to many parameters.
T178 26353-26417 Sentence denotes The mainly parameters which could be changed were bP, bW, and γ.
T179 26418-26658 Sentence denotes Interventions such as wearing masks and increasing social distance could decrease the bP, the intervention that close the seafood market could decrease the bW, and shorten the duration form symptoms onset to be diagnosed could decrease 1/γ.
T180 26659-26783 Sentence denotes All these interventions could decrease the effective reproduction number and finally be helpful to control the transmission.
T181 26784-26874 Sentence denotes Since there are too many parameters in our model, several limitations exist in this study.
T182 26875-27008 Sentence denotes Firstly, we did not use the detailed data of the SARS-CoV-2 to perform the estimation instead of using the data from literatures [3].
T183 27009-27255 Sentence denotes We simulated the natural history of the infection that the proportion of asymptomatic infection was 50%, and the transmissibility of asymptomatic infection was half of that of symptomatic infection, which were different to those of MERS and SARS.
T184 27256-27350 Sentence denotes It is known that the proportion of asymptomatic infection of MERS and SARS was lower than 10%.
T185 27351-27433 Sentence denotes Secondly, the parameters of population mobility were not from an accurate dataset.
T186 27434-27571 Sentence denotes Thirdly, since there was no data of the initial prevalence of the virus in the seafood market, we assumed the initial value of 1/100 000.
T187 27572-27647 Sentence denotes This assumption might lead to the simulation been under- or over-estimated.
T188 27648-27884 Sentence denotes In addition, since we did not consider the changing rate of the individual’s activity (such as wearing masks, increasing social distance, and not to travel to Wuhan City), the estimation of importation of the virus might not be correct.
T189 27885-27951 Sentence denotes All these limitations will lead to the uncertainty of our results.
T190 27952-28210 Sentence denotes Therefore, the accuracy and the validity of the estimation would be better if the models fit the first-hand data on the population mobility and the data on the natural history, the epidemiological characteristics, and the transmission mechanism of the virus.
T191 28212-28223 Sentence denotes Conclusions
T192 28224-28434 Sentence denotes By calculating the published data, our model showed that the transmissibility of SARS-CoV-2 might be higher than MERS in the Middle East countries, similar to SARS, but lower than MERS in the Republic of Korea.
T193 28435-28632 Sentence denotes Since the objective of this study was to provide a mathematical model for calculating the transmissibility of SARS-CoV-2, the R0 was estimated based on limited data which published in a literature.
T194 28633-28699 Sentence denotes More data were needed to estimate the transmissibility accurately.
T195 28701-28714 Sentence denotes Abbreviations
T196 28715-28747 Sentence denotes 2019-nCoV 2019 novel coronavirus
T197 28748-28780 Sentence denotes BHRP Bats-Hosts-Reservoir-People
T198 28781-28811 Sentence denotes R 0 Basic reproduction number
T199 28812-28831 Sentence denotes RP Reservoir-People
T200 28832-28890 Sentence denotes SARS-CoV-2 Severe acute respiratory syndrome coronavirus 2
T201 28891-28920 Sentence denotes WHO World Health Organization
T202 28922-28938 Sentence denotes Acknowledgements
T203 28939-29053 Sentence denotes We thank Qingqing Hu at School of Medicine, University of Utah for her reviewing and editing the English language.
T204 29055-29077 Sentence denotes Authors’ contributions
T205 29078-29242 Sentence denotes TC designed research; TC conceived the experiments, TC, JR, ZZ, QW, JAC, and LY conducted the experiments and analyzed the results; TC and JAC wrote the manuscript.
T206 29243-29294 Sentence denotes All authors read and approved the final manuscript.
T207 29296-29303 Sentence denotes Funding
T208 29304-29423 Sentence denotes This study was supported by Xiamen New Coronavirus Prevention and Control Emergency Tackling Special Topic Program (No:
T209 29424-29439 Sentence denotes 3502Z2020YJ03).
T210 29441-29475 Sentence denotes Availability of data and materials
T211 29476-29491 Sentence denotes Not applicable.
T212 29493-29535 Sentence denotes Ethics approval and consent to participate
T213 29536-29551 Sentence denotes Not applicable.
T214 29553-29576 Sentence denotes Consent for publication
T215 29577-29592 Sentence denotes Not applicable.
T216 29594-29613 Sentence denotes Competing interests
T217 29614-29672 Sentence denotes The authors declare that they have no competing interests.