Within host dynamics of SARS-CoV-2 in humans: Modeling immune responses and antiviral treatments
aa r X i v : . [ q - b i o . P E ] J un Within host dynamics of SARS-CoV-2 in humans: Modelingimmune responses and antiviral treatments
Indrajit Ghosh a Agricultural and Ecological Research Unit, Indian Statistical Institute, Kolkata, West Bengal 700108,India
Abstract
In December 2019, a newly discovered SARS-CoV-2 virus was emerged from China andpropagated worldwide as a pandemic, resulting in about 35% mortality. In the absenceof preventive medicine or a ready to use vaccine, mathematical models can provide usefulscientific insights about transmission patterns and targets for drug development. In thisstudy, we propose a within-host mathematical model of SARS-CoV-2 infection consid-ering innate and adaptive immune responses. We analyze the equilibrium points of theproposed model and obtain an expression of the basic reproduction number. We thennumerically show the existence of a transcritical bifurcation. The proposed model is cali-brated to real viral load data of two COVID-19 patients. Using the estimated parameters,we perform global sensitivity analysis with respect to the peak of viral load. Finally, westudy the efficacy of antiviral drugs and vaccination on the dynamics of SARS-CoV-2infection. Our results suggest that blocking the production of the virus by infected cellsdecreases the viral load more than reducing the infection rate of healthy cells. Vacci-nation is also found useful but during the vaccine development phase, blocking virusproduction from infected cells can be targeted for antiviral drug development.
Keywords:
SARS-CoV-2, Immune response, Model calibration, Numerical simulation,Treatments.
1. Introduction
Coronaviruses are a large group of viruses that have the potential to transmit be-tween hosts. These are enveloped in positive-sense, non-segmented RNA viruses belong-ing to the Coronaviridae family (Nidovirales order) and widely distributed in humans andother mammals [1]. The virus is responsible for a range of symptoms including fever,cough, and shortness of breath [1]. Some patients have reported radiographic changesin their ground-glass lungs, healthy or lower than average white blood cell lymphocyte, Corresponding author. Email: [email protected], indrajitg [email protected]
Preprint submitted to Elsevier June 30, 2020 nd platelet counts; hypoxaemia; and deranged liver and renal function. Since first dis-covery and identification of coronavirus in 1965, three significant outbreaks occurred,caused by emerging, highly pathogenic coronaviruses, namely the 2003 outbreak of ”Se-vere Acute Respiratory Syndrome” (SARS) in mainland China [2, 3], the 2012 outbreakof ”Middle East Respiratory Syndrome” (MERS) in Saudi Arabia [4, 5], and the 2015outbreak of MERS in South Korea [6, 7, 8]. These outbreaks resulted in SARS andMERS cases confirmed by more than 8000 and 2400, respectively [9]. A newer and ge-netically similar coronavirus is responsible for the coronavirus disease 2019 (COVID-19).The virus is named SARS-CoV-2. Despite a relatively lower case fatality rate comparedto SARS and MERS, the COVID-19 spreads rapidly and infects more people than theSARS and MERS. Despite strict intervention measures implemented in the region wherethe COVID-19 was originated, the infection spread locally and elsewhere very rapidly.COVID-19 has been declared a pandemic by the World Health Organization in January2020. Since its first isolation in Wuhan, China in December 2019, it has caused out-break with more than 10 million confirmed infections and above 500 thousand reporteddeaths worldwide as of 28 June 2020. The affected countries around the globe are fight-ing the virus by implementing social distancing and isolation strategies. Unfortunately,the COVID-19 has neither a preventive medicine nor a ready to use vaccine. Multi-ple approaches are adopted in the development of Coronavirus vaccines; most of thesetargets the surface-exposed spike (S) glycoprotein or S protein as the primary inducerof neutralizing antibodies [10, 11]. In fact, either monoclonal antibody or vaccine ap-proaches have failed to neutralize and protect from previous coronavirus infections [12].Therefore, individual behaviour (e.g. early self-isolation and social distancing), as well aspreventive measures such as hand washing, covering when coughing, are critical to con-trol the spread of COVID-19 [13]. However, researchers have been putting more effortinto finding a solution to this pandemic situation [14, 15, 16].In addition to medical and biological research, theoretical studies based on math-ematical models may also play an important role throughout this anti-epidemic fightin understanding the epidemic character traits of the outbreak, in having to decide onthe measures to reduce the spread and in understanding within-host patterns of virustransmission. While there are many mathematical models developed at an epidemiolog-ical level for COVID-19 [17, 18, 19, 20], there are very few within-host level studies tounderstand SARS-CoV-2 replication cycle and its interactions with the innate and adap-tive immune responses [21, 13]. In these few previous studies, authors studied targetcell models and target cell models with eclipse phase. Therefore, detailed research withimmune responses is necessary for the understanding of SARS-CoV-2 spread inside thehuman body. The human immune system is comprised of innate and adaptive immuneresponses. While the adaptive immune system is both fast and effective at targeting2nvasions by previously encountered pathogens, its role in host defence in the first daysof a new infection is secondary to that of the innate immune system.Motivated by this discussion, we aim to develop a within-host mathematical model ofSARS-CoV-2 infection considering human immune responses. This model can be used asa basis for understanding characterized patterns of disease severity in humans. Moreover,we intend to use real viral load data from COVID-19 positive patients to calibrate theproposed model so that the parameters are realistic for further inference. The maingoal is to compare the efficacy of various antiviral drugs and identify the most beneficialtarget.The rest of the paper is organized as follows: in Section 2, we formulate the com-partmental model of within human SARS-CoV-2 transmission; the equilibrium pointsof the proposed model are analyzed and the basic reproduction number is obtained inSection 3; viral load time series, transcritical bifurcation, fitting model to real data andglobal sensitivity analysis are presented in Section 4; in Section 5, we study the efficacyof antiviral drugs and vaccination; finally, the obtained results are discussed in Section6.
2. The mathematical model
A deterministic ordinary differential equation model describing cell–virus–immuneresponse interaction dynamics of SARS-CoV-2 infection is being formulated. Time-dependent state variables are taken to represent the compartments. A general mathe-matical model for the underlying dynamics of virus-host cell interaction has been studiedin this context [21, 13]. However, the basic principles that underlay models of virusdynamics are as follows: Healthy uninfected cells, H ( t ), are infected when they meetfree viruses, V ( t ). Infected cells, I ( t ), produce new virus particles that leave the celland find other susceptible target cells. Whenever a human is infected with SARS-CoV-2, his innate and adaptive immune responses work together to neutralize the threat ofSARS-CoV-2 infection [22, 23, 16]. The innate immune response works non-specificallyand immediately after the viral attack. Cells and proteins of the innate immune systemare ever-present in a healthy host and can respond to invading pathogens within the firstminutes and hours of infection [24]. This system is of great importance in the sense thatit is preventing the establishment of new infections during the activation time of theadaptive immune system. It is believed that Cytokines are an essential component of theimmune system [25]. They are a family of small soluble proteins secreted by differentcells. They can be loosely classified into one of four families: the haematopoietins, theimmunoglobin superfamily, the tumour necrosis factor family and the interferons (IFN).Cytokines modulate the balance between innate and adaptive immune responses. TheIFNs are perhaps the most critical cytokines in the initial innate response to viral in-3ection. They are classified into two types: IFN- α (a family of related proteins) andthe single protein IFN- β together form type I; IFN- γ is the sole and unrelated type IIIFN. IFN- α and IFN- β are secreted by cells in response to viral infection and promotean antiviral response in otherwise susceptible cells. Cytokines C(t) is vital in inhibitingviral replication and modulating downstream effects of the immune response. Specificcytokines activate natural killer (NK) cells N(t), which play an essential role in killingvirus-infected cells. As in [26, 27], the rate of NK cells increment by cytokines is takenas rC , whereas NK cells die at a rate µ . However, Against the inhibiting mechanism ofcytokines, the viruses often target the JaK/STAT pathway to decrease the production ofIFNs. This mechanism, known as immunosupression, is observed for SARS-CoV-2 [28].The functional form of a decrease in the cytokine production rate is assumed to be k I γV .Meanwhile, cytokines also activate the adaptive immune system, mainly the cytotoxicT-lymphocytes T(t) at a rate λ . Interleukin-2 (IL-2) is a type of cytokine signalingmolecule in the immune system that is very important to activate T-cells. T-cells findsvirus infected cells and kill them at a rate p . T-cells subsequently activate B-lymphocytesB(t) at a rate λ to produce antibody against the virus. B-cells mainly secrete IgM andIgG antibodies that are released in the blood and lymph fluid, where they specificallyrecognize and neutralize the SARS-CoV-2 viral particles [25, 22]. Meanwhile, antibodylevels A(t) are increasing with the aim of halting infection (and in future providingprotection against a subsequent infection). A schematic flow diagram of the model isdepicted in Fig. 1.Finally, the cell–virus–immune response interaction dynamics of SARS-CoV-2 infec-tion are governed by the following system of differential equations: dHdt = Π − βHV − µ H,dIdt = βHV − p T I − p N I − µ I,dVdt = k I − p CV − p AV − µ V,dCdt = k I γV − µ C, (2.1) dNdt = rC − µ N,dTdt = λ CT − µ T,dBdt = λ T B − µ B,dAdt = G ( t − τ ) ηB − p AV − µ A. igure 1: Schematic diagram of the proposed model. The blue arrows indicate production, black arrowsindicate activation and orange ones show inhibition by different cells. The time delay τ introduced through the Heaviside step function [29], is the timeperiod that is required for the first production of antibodies after the T-lymphocytesand B-lymphocytes interact. This delay is biologically significant since the production ofantibodies after the virions have associated with the B-lymphocytes is a complex processinvolving multiple steps. The B-cells have to undergo differentiations before they can betransformed into the plasma cells capable of producing antibodies [30]. The Heavisidestep function G ( t ) is defined as follows, G ( t − τ ) = 1 , if t > τ = 0 , if t < τ The model 2.1 has initial conditions given by: H (0) = H ≥ I (0) = I ≥ V (0) = V ≥ C (0) = C ≥ N (0) = N ≥ T (0) = T ≥ B (0) = B ≥
0, and A (0) = A ≥
3. Equilibria and Basic reproduction number
There are four type of equilibia of the system (2.1), namely,5 able 1: Parameters used in model 2.1
Parameter Symbol value/Range ReferenceProduction rate of healthy cells Π 4 × cells ml − day − [31]Rate at which healthy cells areconverted to infected cells β (5 – 561) × − ml (RNAcopies) − day − [13]Strength of immunosupresion γ − AssumedRate at which T-cells destroy in-fected cells p − day − [32]Rate at which viral particles areneutralized by cytokines p (0 – 1) ml cells − day − EstimatedRate at which viral particles areneutralized by antibodies p (0 – 1) ml molecules − day − EstimatedRate at which virus neutralize an-tibodies p × − ml (RNA copies) − day − [31]Rate at which infected cells arediminished by NK cells p × − ml cells − day − [27]Production rate of virus from in-fected cells k (8.2 – 525) day − [13]Production rate of cytokines k (0 – 10) day − AssumedActivation rate of NK cells r − [27]Activation rate of T cells λ − day − [25]Activation rate of B cells λ − day − [25]Rate at which antibodies are pro-duced η (0 - 1) day − [30]Natural death rate of Healthycells and protected cells µ − [25]Natural death rate of infectedcells µ (0 – 1) day − AssumedClearance rate of virus µ (0 – 1) day − EstimatedNatural death rate of cytokines µ − AssumedNatural death rate of NK cells µ − [27]Natural death rate of T cells µ − [25]Natural death rate of B cells µ − [31]Natural death rate of antibodies µ − [25]Time delay for antibody produc-tion τ E = ( Π µ , , , , , , , E = ( H , I , V , , , , , H = Π µ R , I = µ µ βk ( R −
1) and V = µ β ( R − R = Π βk µ µ µ . Clearly, this equilibrium exists only when R > E = ( H , I , V , C , N , , , Q = βH V ) H = Π − Qµ , N = rCµ , I = Qµ + p N , V = γ h k I µ C − i and C is given by the roots of the following cubicequation p p µ rµ C + ( µ µ p + µ µ p rµ ) C + ( µ µ µ + µ γk Q − k p Q ) C − k µ Q = 0. Note that, irrespective of the sign of the coefficient of C , Descartes’ rule of signensure existence of exactly one positive root whenever k I µ C > E = ( H , I , V , c , N , T , B , A ),where (assume, Q = βH V ) H = Π − Qµ , I = µ µ R λ k , V = γ [ R − C = µ λ , N = rC µ , T = µ λ , B = A η [ p V + µ ] and A = p V [ R − R = λ k Qµ µ ( p µ λ + rp µ λ µ + µ )and R = γλ k k QR µ µ ( λ µ + p µ )( R − . It can be noted that this equilibrium exists only when R > R > Theorem 3.1.
The DFE E of the system (2.1) is locally asymptotically stable, if R < ,and unstable if R > , where R = Π βk µ µ µ . (3.1) Proof.
The Jacobian of the system (2.1) at E is given as J ( E ) = − µ − β Π µ − µ β Π µ k − µ k − µ r − µ − µ − µ
00 0 0 0 0 0 G ( t − τ ) η − µ (3.2)7learly, − µ , − µ , − µ , − µ , − µ and − µ are eigenvalues of this Jacobean matrixand other two eigenvalues are given by the roots of the following equation C (Λ) := Λ + a Λ + a = 0 (3.3)where a = µ + µ a = µ µ (1 − R ) (3.4)Therefore, for R <
1, the conditions for the Routh-Hurwitz criteria are satisfied andhence DFE is locally asymptotically stable. Now if R >
1, then a < C ( λ ) = 0will possess a positive real solution. Therefore the DFE will be unstable for R >
4. Numerical Simulation
In this section, important properties of the proposed model are investigated numeri-cally. Using different parameter settings, time series and threshold analysis is performed.Moreover, the agreement of the model solution with real data is explored. Through outthis section the following set of initial conditions is used unless stated H (0) = 4 × cells per ml, I (0) = 3 × − cells per ml, V (0) = 357 RNA copies per ml, C = 0 cellsper ml, N = 100 cells per ml, T = 500 cells per ml, B = 100 cells per ml and A = 0molecules per ml (most of the initial conditions are taken from [25, 31]). We first study the time series of the viral load and antibody count. In Fig. 2, the viralload and antibody are plotted. The viral load time series experiences a peak betweensixth and seven days post infection. However, as soon as the adaptive immune response isactivated (after τ = 7 days), a sharp decrease is observed in the viral load. On the otherhand, the antibody count starts to rise after 7 days post infection and shows saturatedtype behaviour. 8 Time (Days) V i r a l l oad × a Time (Days) A n t i bod y c oun t b Figure 2: Time evolution of (a) viral load ( V ) and (b) antibody count ( A ) of the model 2.1. All theparameters are taken from Table 1 except β = 2 × − , µ = 0 . µ = 0 . p = 0 . p = 0 . k = 500, k = 5, η = 0 .
05 and τ = 7. Further, we study the threshold for R . It is observed that R = 1 acts as a criticalvalue for the persistence of virus particles. The virus particles converges to the DFE ofthe model 2.1 for R < R crosses unity. This type of phenomenon is called forward bifurcation where the twoequilibrium points switches their stability at a critical value. The diagram is depicted inFig. 3. This also ensure that if we vary other parameters involved in the expression of R , the same type of phenomenon occurs. Thus, in turn parameters such as β and k can be reduced so as to reduce R below unity. SARS-CoV-2 viral load data are obtained from Wolfel et al. [34]. They studiedpatients from a hospital in Munich, Germany. They reported Daily measurements ofviral load in sputum, pharyngeal swabs and stool for 9 patients. Among these patients,there were two patients (namely, patient A and patient B) for whom the growth phaseof sputum data was captured. We therefore utilized these two datasets for our analysis.The data was collected from Wolfel et al. [34] using a online software [35].The solution curve of viral load ( V ( t )) is fitted to data using the built-in (MATLAB,R2018a) simplex algorithm to minimize the sum of squares difference between simulatedindicators and data. We used the MATLAB function ‘fminsearchbnd’ to perform theoptimization. During the computation, 100 different starting points in parameter spacewere chosen using Latin Hypercube Sampling to ensure consistency and uniqueness ofthe parameter estimates. The fitting is displayed in Fig. 4(a) for patient A and in Fig.4(b) for patient B. The fixed parameters are taken from Table 1 with µ = 0 . k = 5and η = 0 .
05. The initial conditions are taken as mentioned in the beginning of Section4. We estimated five parameters directly related to viral load of a patient viz., β , k , p , p and µ . The estimated parameters for patient A are found to be β = 1 . × − , k = 379, p = 0 . p = 0 . µ = 0 . .2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 R V i r a l l oad a t equ ili b r i u m × Figure 3: Forward bifurcation diagram with respect to basic reproduction number. All the fixed param-eters are taken from Table 1 with µ = 0 . µ = 0 . p = 0 . p = 0 . k = 500, k = 5, η = 0 . τ = 7 and 10 − < β < − , B are obtained as β = 5 . × − , k = 128, p = 0 . p = 0 . µ = 0 . We performed global sensitivity analysis to identify most influential parameters withrespect to the maximum size (or alternatively, the peak of load) of virus particles ( V max )in 3 months time frame. Partial rank correlation coefficients (PRCCs) are calculated andplotted in Fig. 5. Nonlinear and monotone relationship were observed for the parameterswith respect to V max , which is a prerequisite for performing PRCC analysis. FollowingMarino et. al [36], we calculate PRCCs for the parameters β , k , k , µ , µ , p , p , γ and η . The base values for the parameters β , k , p , p and µ are taken as the average ofestimated parameters of patient A and patient B. The other base values are µ = 0 . k = 5, γ = 0 . η = 0 .
05. For each of the parameters, 500 Latin Hypercube Sampleswere generated from the interval (0.5 × base value, 1.5 × base value).It is observed that the parameters β , k and γ has significant positive correlationswith V max . This indicates that the production rate of virus particles from infected cellswill increase the chance of larger infection propagation. Besides, the infection rate andthe immiunosuppresion rate are positively correlated with the peak of viral load. On theother hand, the natural death rate of infected cells and death rate of virus particles willhave significant negative correlation with V max . The production rate of cytokines is also10 Time (Days) l og ( V i r a l l oad i n s pu t u m ) ModelSputam data(patient A) a Time (Days) l og ( V i r a l l oad i n s pu t u m ) Model Sputum data (patient B) b Figure 4: Fitting model solution to (a) patient A data and (b) patient B data. negatively correlated with V max . These results reinforces the fact that β and k are verycrucial for reduction of viral load.
5. Model with antiviral treatment
Antiviral drugs can be used to slow SARS-CoV-2 infection or block production ofvirus particles. These drugs will necessarily save the lives of many severely ill patientsand will reduce the time spent in intensive care units for patients, vacating hospital beds.Antiviral medications will, in turn, inhibit subsequent transmission that could happen ifthe drugs were not given. However, to analyze the effect of antiviral treatment, we con-sider drugs can block infection and/or production of virus particles. Many studies havesuggested various existing compounds for testing [16, 37, 38] as SARS-CoV-2 antiviraldrug, but World Health Organization (WHO) is focusing on the following four therapies:an experimental antiviral compound called remdesivir; the malaria medications chloro-quine and hydroxychloroquine; a combination of two HIV drugs, lopinavir and ritonavir;and that same combination plus interferon-beta, an immune system messenger that canhelp cripple viruses [39].Following Zitzmann et al. [40], we incorporate antiviral drug treatment in the pro-posed model (2.1). The modified system with antiviral treatment is given by11 k k µ µ p p γ η -1-0.8-0.6-0.4-0.200.20.40.60.81 P RCC ** * * significant (p-value < 0.05) *** *
Figure 5: Effect of uncertainty of the model (2.1) on the peak of viral load. Parameters with significantPRCC indicated as ∗ (p-value < µ = 0 . k = 5, η = 0 .
05 and τ = 7. dHdt = Π − (1 − ǫ ) βHV − µ H,dIdt = (1 − ǫ ) βHV − p T I − p N I − µ I,dVdt = (1 − ǫ ) k I − p CV − p AV − µ V,dCdt = k I γV − µ C, (5.1) dNdt = rC − µ N, (5.2) dTdt = λ T C − µ T,dBdt = λ BT − µ B,dAdt = G ( t − τ ) ηB − p AV − µ A. From Fig. 6, it can be noted that increase in ǫ reduces the peak of viral load but theduration of high viral load remains same. On the other hand, increase in ǫ significantly12 Time (days) V i r a l l oad × ǫ =0 ǫ =0.4 ǫ =0.8 a Time (days) V i r a l l oad × ǫ =0 ǫ =0.4 ǫ =0.8 b Figure 6: Effect of antiviral drugs that (a) reduce infection or (b) blocks virus production. The timeseries of viral load is presented for different values of ǫ and ǫ . The fixed parameters are taken fromTable 1 with µ = 0 . k = 5, η = 0 .
05 and τ = 7. Other fixed values are taken to be the average ofestimated parameters for patient A and patient B. reduce both peak of viral load and duration of high viral load. Thus, we conclude thatblocking the virus production from infected cells is a more suitable target for antiviraldrug development.Finally, we study the effect vaccination in the viral dynamics of SARS-CoV-2 inhumans. A vaccine is a biological preparation that provides active acquired immunityto a particular infectious agent. Thus if an individual is vaccinated, there will be nodelay in the development of antibody. Therefore, the delay term τ is taken to be zero forvaccinated individuals (see Fig. 7). It is observed that vaccination not only reduces theviral load in healthy patients but also reduces the duration of high viremia.Overall, for antiviral drug target, blocking virus production is more fruitful in termsof viral load reduction and vaccination will also be effective.
6. Discussion and conclusion
In this study, we have proposed and analyzed a compartmental model of SARS-CoV-2 transmission within the human body. The much needed innate and adaptive immuneresponses are incorporated into the model. The eight-dimensional model has four types ofequilibrium points. The existence criterion for each type of equilibria is presented. Fromthe local stability of the DFE, the expression for basic reproduction number is obtained.This number is very crucial for the persistence of the virus in the long run. However,the short-term dynamics of the viral load is studied using various numerical techniques.During time series analysis, we observed that the viral load time series experiences apeak between sixth and seven days post-infection, followed by a sharp decrease due toactivation of adaptive immune response (see Fig. 2). A forward bifurcation of equilibriawith respect to the basic reproduction number is observed and depicted in Fig. 3. Thisalso ensures that if we suitably vary parameters involved in the expression of R , the13 Time (days) V i r a l l oad × τ = 0 τ = 7 Figure 7: Viral load time series for different values of τ for the model (2.1). The fixed parameters aretaken from Table 1 with µ = 0 . k = 5, η = 0 .
05 and τ = 7. Other fixed values are taken to be theaverage of estimated parameters for patient A and patient B. same type of phenomenon occurs. Thus, in turn, parameters such as β and k can bedecreased to reduce R below unity and ensure local asymptotic stability of DFE.We used daily measurements of SARS-CoV-2 viral load in sputum for two patients[34] from a hospital in Munich, Germany. Using the estimated parameters, the globalsensitivity analysis of several model parameters with respect to peak viral load is per-formed. The results indicate that the production rate of virus particles from infected cellswill increase the chance of more significant infection propagation. Besides, the infectionrate and the immiunosuppresion rate will increase the peak of viral load. Additionally,the natural death rates of infected cells and the death rate of virus particles will havea significant negative correlation with the peak of viral load. The production rate ofcytokines is also negatively correlated with the peak of viral load. These results reinforcethe fact that β and k are very crucial for the reduction of viral load.Antiviral drugs can be used to slow SARS-CoV-2 infection (or reduce β ) or block theproduction of virus particles (or reduce k ). Results suggest that a decrease in β reducesthe peak of viral load but the duration of the high viral load remains the same. On theother hand, a decrease in k significantly reduce both peak of viral load and period ofhigh viral load. Thus, we conclude that blocking virus production from infected cells isa more suitable target for antiviral drug development. Moreover, vaccination can reduce14he viral load in healthy patients and also reduce the duration of high viremia in the body.But vaccine development is a complicated task; therefore, during the vaccine developmentphase, blocking virus production from infected cells can be targeted for antiviral drugdevelopment.Researchers have been putting more effort to develop a vaccine to tackle COVID-19 [10, 11]. The journey has started with the first clinical trial just two months afterthe genetic sequence of the virus. The mathematical model developed in this papercan be improved by adding more detailed data to reveal prophylactic and therapeuticinterventions. Our theoretical findings should be tested clinically for the implementation.Further insights into immunology and pathogenesis of SARS-CoV-2 will help to improvethe outcome of this and future pandemics. References [1] Chaolin Huang, Yeming Wang, Xingwang Li, Lili Ren, Jianping Zhao, Yi Hu,Li Zhang, Guohui Fan, Jiuyang Xu, Xiaoying Gu, et al. Clinical features of patientsinfected with 2019 novel coronavirus in wuhan, china.
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