Proc. Natl. Acad. Sci. USA
Vol. 93, pp. 4398-4402, April 1996
Viral dynamics in hepatitis B virus infection
(lamivudine/antiviral treatment/liver/viral turnover/mathematical model)
MARTIN A. NOWAK*t, SEBASTIAN BONHOEFFER*, ANDREW M. HILLt, RICHARD BOEHMEt, HOWARD C. THOMAS§,
AND HUGH MCDADEt
*Department ofZoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, United Kingdom; tGlaxo Research and Development, Greenford Road,
Greenford, Middlesex, UB6 OHE, United Kingdom; and §Department of Medicine, St Mary's Hospital Medical School, Imperial College of Science, Technology,
and Medicine, London, W2 1PG, UnitedKingdom
Communicated by Richard Southwood, University of Oxford, Oxford, United Kingdom, December 13, 1995 (received for review October 24, 1995)
infections with the reverse transcriptase inhibitor lamivudine
leads to arapiddecline inplasmaviremia andprovidesestimates
for crucial kinetic constants ofHBVreplication.We find that in
persistentlyinfectedpatients,HBVparticlesare cleared from the
plasma with a half-life of -1.0 day, which implies a 50%daily
turnover ofthe free virus population.Total viral release into the
peripheryis -1011 virusparticles per day. Althoughwe have no
direct measurement ofthe infected cell mass,we can estimate the
turnover rate ofthese cells in twoways: (i) by comparingthe rate
of viral production before and after therapy or (ii) from the
decline of hepatitis B antigen during treatment. These two
independent methods give equivalent results: we find a wide
distribution of half-lives forvirus-producing cells, rangingfrom
10 to 100daysin differentpatients,whichmayreflect differences
in rates of lysis of infected cells by immune responses. Our
analysis provides aquantitative understandingofHBVreplica-
tiondynamicsin vivo and hasimplicationsfor theoptimal timing
ofdrugtreatment andimmunotherapyin chronicHBV infection.
This study also represents a comparison for recent findings on
thedynamicsofhumanimmunodeficiencyvirus (HIV) infection.
The totaldailyproductionofplasmavirus is,onaverage, higher
in chronic HBV carriers than in HIV-infected patients, but the
half-life ofvirus-producing cells is much shorter in HIV. Most
strikingly,there is no indication of drug resistance in HBV-
infected patients treated forup to 24 weeks.
Treatment of chronic hepatitis B virus (HBV)
More than 250 million people worldwide are chronically
infected with hepatitis B virus (HBV), and 25-40% of these
will die from liver cirrhosis or primary hepatocellular carci-
noma (1, 2). Chronic HBV infection is often the result of
exposure early in life, leading to viral persistence in the
absence ofstrong antibodyor cellular immune responses (3).
Therapy of HBV carriers can aim to either inhibit viral
replication or enhance immunological responses against the
virus, or both (4).
The nucleoside analogue, (-)-2'-deoxy-3'-thiacytidine
(lamivudine), originally developedas an anti-human immuno-
deficiencyvirus (HIV) drug, haspotent inhibitoryeffects on
HBVreplicationin vivo(5, 6, 31).Chronic HBV carriers were
treated with various doses oflamivudine. Plasma virus load was
quantified at frequent times before, during, and after treat-
mentusing quantitative methods for determiningviral DNA.
In the first study, 45 patients were treated for 28 days; in a
subsequent study, 50 patientswere treated for 24 weeks. Fig.
1A shows plasma virus changes in six patients treated for 28
days.After onset oftherapyviral levels declinerapidly,but as
soon as the drug is withdrawn, virus returns. Fig. 1B shows
changesinplasma viremia, hepatitisBantigen (HBeAg), and
serum alanine aminotransferase (ALT)in sixpatients treated
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for 24 weeks.Againwe observe rapid decline inplasmavirus
load, which falls below detection limit in almost all patients
within 2-4 weeks, and again in most patients, virus resurges
rapidly as soon as the drug is withdrawn. HBeAg is a viral
protein produced byinfected cells; itsproductionis notdirectly
inhibited by lamivudine (7), and changes in the serum con-
centration can therefore reflect changes in infected liver cell
mass. ALT is released from damaged liver cells; thus it is an
indicator of the level of cell damage and death. HBeAg and
ALT decline slowly during longterm lamivudine treatment.
Therapeuticallyinduced HBeAg seroconversion, seen during
successful interferon a therapy and thought to represent the
lysis of infected cellsbythe host's immune response, is not a
feature of lamivudine treatment.
For aquantitative analysis of these observations, we design
a simple but natural mathematical model based on ordinary
differential equationsfor uninfected cells, x, infected cells, y,
and free virus, v:
Uninfected, susceptiblecells areproducedat a rate, A, which
may be constant or depend on the total population size of
uninfected and infected cells. Uninfected cells die at rate dx,
and become infected at rate bvx, where b is the rate constant
describingthe infectionprocess.Infected cells areproducedat
rate bvx and die at rate ay. Free virions are produced from
infected cells at rate ky and are removed at rate uv. Strictly
speaking,thedecayrate of free virus should also be a function
of the uninfected(and infected)cellpopulation,but weexpect
the leadingterm of viraldecayto beindependentofchanges
in the host cell population. Therefore it is a reasonable
assumption to treat u as a constant. The magnitude of the
parameters a, b, k, and u will be determined by antiviral
immune responses. In the absence of treatment the system
convergesto asteadystate ofpersistent infection, providedthe
basicreproductiveratio of thevirus, Abk/(adu)isgreaterthan
1. This condition islikelyto be fulfilled ifpatientshave weak
immuneresponses againstfree virus(lowu)oragainstinfected
cells (low a). Hence, in our simple model weak immune
responses predispose to carrier state.
In the replication cycle of HBV, the viral reverse tran-
scriptase is responsible for the synthesis of new HBV DNA
from the pregenomic mRNA template (8, 9). Therefore,
lamivudine canpreventtheproductionof new virusparticles
is also essential for completing the double-stranded circular
=0). But the viralpolymerase
Abbreviations: HBV, hepatitis B virus; HIV, human immunodefi-
ciency virus; HBeAg, hepatitisB antigen; ALT, alanine aminotrans-
ferase; cccDNA, covalentlyclosed circular DNA.
tTo whom correspondence should be addressed.
Medical Sciences: Nowak et al.
Proc. Natl. Acad. Sci. USA 93 (1996)
, ,------- Patient
at various doses(5, 20, 100, 300, and 600mg per day)for 28days. Plasma virus was determined atdays 0, 2, 7, 14, 21, 28, 35, 42, 56, 70, and 84.
Squaresindicate virus load below detection limit.(B)Viral load(circlesandsquares), HBeAg (triangles),and ALT levels(crosses)in sixpatients
treated for 24 weeks. In thisstudy, a total of 50patientsreceived lamivudinetherapyat 25, 100, and 300mg per day. Plasma virus was obtained
at weeks 0, 2, and 4, andsubsequently every4 weeks until week 48. For our analysisweonlyusedpatientswho received at least 100mg per day.
Serum HBV DNA wasquantified usingthe Abbott Genostics solutionhybridization kit.HBeAgwasquantified usingthe Kodak Amerlite kit.
DNA before migration to the cell nucleus (10), and hence
there is some evidence that lamivudine can prevent the
infection of new cells (b=0) (11). This implies that during
treatment free virus is decaying exponentially according to
v(t)=voe-ut. Similarly, infected cells aredecaying exponen-
tially accordingtoy(t)=yoe-at. Herevoandyoindicate free
virus and infected cells at the beginning oftherapy. If lami-
(A)Rapidviral decline inresponseto lamivudine treatment in sixpatients.In thisstudy,a total of45patientsreceived lamivudinetherapy
vudine does noteffectively preventinfection of newcells, then
the aboveequations are stillvery good approximations, pro-
vided u is substantially larger than a (which will be shown
below).Therefore ouranalysisdoes notrelyon theassumption
that lamivudine also blocks new infection. From the decline of
free virus we can estimate thedecayrate u. Before treatment,
steady state of free virus implies kyo=uvo. We know vo,
Medical Sciences: Nowak et al.
hence we can estimatekyo,which is the total virusproduction
From the 1-month studywe can estimate the initial rate of
virus declineduringthe first 2daysof treatment. We obtain an
average of u = 0.67 per day (o-=0.32, n =23), which
corresponds to a half-life time(Ti/2)of 1.0 day. Hence, in the
absence of treatment =50% of theplasmavirus isreplenished
every day. The total serum virus load (for 3 liters ofserum)
before treatment varies in differentpatients rangingfrom 1010
to 1012 particles, with anaverageof 2.2 x 1011(o-= 2.6 x 1011,
n =45). Consequently, the total amount of plasma virus
production follows a wide distribution with an average of 1.3
x 101l particles per day (a= 8.2 x 1010, n =23). These
differences are likely to reflect different population sizes of
virus-infected cells in individual patients. Plasma virus levels
usually correlate with abundance of infected cells as deter-
mined by histological examination of the liver (12).
Virus decline during treatment is not strictly exponential
(see Fig. 1).This can be explained bytheassumption that the
efficacy of the drug is not 100%. Assuming a certain efficacy
p,viral decay occurs according to v(t)=vo(l
Fittingthis functionprovidesan estimate for theefficacyofthe
drug at various doses. We find that fordailydoses of 20, 100,
300, and 600mg,viralreplicationis inhibitedby 87, 97, 96, and
When therapy is withdrawn, virus resurges according to
dv/dt =ky-uv. Hence, the initial virusgrowthrate can be
where v1 andyi indicate the levels of free virus and infected
cells at the end oftherapy.We know v1bydirectmeasurement,
and we have determined the decay rate, u; hence we can
estimate kyl, which is the rate of virus production from
infected cells at the end oftherapy. Comparing kyo andkyl
gives an estimate for the decay rate of infected (virus-
producing) cells, a, and consequently, their half-life. This
method requires the initialgrowth rate of virus aftertherapy
hasstoppedsinceyis treated as a constant. Theapproximation
is accurate if virus load is determined early after the end of
treatment. In our study, treatment was withdrawn after 28
days, and virus load was determined at days 28 and 35. We
obtain anaveragedecline of a = 0.043per day (oa=0.036, n
=20) corresponding to aTi/2of 16 days. In differentpatients
half-lives range from about 10 to 100 days.
The broad distribution ofturnover rates ofinfected cellsmay
be a consequence ofheterogeneity of the immune response
against infected cells in different patients (13, 14). Damaged
liver cells release ALT, and henceplasmaALT levels should
providesome crude estimate for the amount ofcell death in the
liver. If most cell damage is caused by immune responses
directed to infected cells(15),then ALT levelsprovide some
estimate for the strength of the immunological response
againstHBV. We find apositivecorrelation between thedecay
rate of infected cells and thepretreatmentALT levelamong
different patients (Fig. 2). This supports our hypothesis that
thevariabilityof celldecayrates reflects differentstrengthsof
anticellular immune responses and is not simply caused by
fluctuations in measurement or inaccurate approximation.
In thesubsequent study, treatment continued for 24weeks,
butsamplingwas lessfrequent (thefirst timepointsafter 2 and
4 weeks, thenevery4weeks), and we cannot obtain accurate
estimates of the viral or cellular decay rates with the above
methods. However, we can obtain anindependent estimate of
the turnover of infected cells from the initialdecayofHBeAg.
Reverse transcriptase inhibitors such as lamivudine have no
direct effect on the synthesis and secretion ofHBeAg, which
is derived from mRNA transcribed from existing covalently
closed circular DNA (cccDNA) molecules of HBV within
infected cells. The capacity of the infected host to synthesize
this protein is dependent on the rate of infection of cells
(inhibited by lamivudine)and the rate oflysisof infected cells
(not inhibited by lamivudine) and dependent on immune
the28-day studythedecay rate, a, was estimatedby comparingthe rate of virusproductionbefore and after treatment(at days0 and28).For the
24-weekstudya was estimated from the initial decline ofHBeAgover the first 2 weeks. ASpearmanrank correlationgivesa correlation coefficient
of r=0.61 (P=0.007) for the28-day study, and r=0.50 (P
rates a suggests that the wide distribution of calculated a values does reflect biological heterogeneity (rather than measurementuncertainty);
different patients appear to have different immune responses againstinfected cells. The symbols reflect patientswith differentdaily dosageof
lamivudine. Squares, 100 mg; circles, 300 mg; triangles, 600 mg.
Correlation between initial serum ALT level before treatment and estimateddecayrate ofvirus-infected cells, a, duringtreatment. For
=0.005) for the 24-weekstudy.The correlation between ALT levels anddecay
Proc. Natl. Acad. Sci. USA 93 (1996)
Proc. Natl. Acad. Sci. USA 93(1996)
recognitionof these cells. Hence the initialdecayofHBeAgin
patients takinglamivudine should reflect thedecayof infected
hepatocytes. Duringthe first 8 weeks of treatment we observe
anaverage decline of a = 0.053 per day (ao=0.039, n =29),
which corresponds to a T,/2of 13 days. This is in agreement
with ourpreviousestimate.Againthere is a wide distribution
of half-lives and we find astrongcorrelation betweendecayof
infected cells andALT levelsamongdifferentpatients (Fig. 2).
After 24 weeks of treatment, patients were followed for
another 24 weeks. Interestingly, there is a strong capacity in
individual patients to return to the pretreatment steady-state
level after these 48 weeks.Fig.3 showsplasmavirus load, ALT
levels, and HBeAg levels for each patient at time 0 and after
48 weeks. Whatever factors-e.g., efficacy of antiviral and
anticellular immuneresponses-determinetheparticular pre-
treatmentsteady-statelevel ofplasma virus, HBeAg,andALT
in individualpatients,it isinterestingto note that these factors
haveappearentlynotchangedover the time course of48weeks
in most patients.
We also analyzed data from a cohort ofJapanese patients,
where treatment continued for 28 days and serum virus load
l l0 ll
chronic HBV infection. Patients were treated for 24 weeks and were
subsequentlyfollowed for another 24 weeks. Thefigureindicates virus
load, HBeAg,and ALT beforetherapy (x axes)versus after 48 weeks
(y axes).In eachdiagram,eachpatientis indicatedbyapoint;different
symbolsreflect differentdaily dosagesof lamivudine(squares,100mg
andcircles, 300mg).Mostpointslie close to thediagonal indicating
thetendencyto return to thepretreatmentlevel. Units: virus load in
particles/ml, HBeAginunits/ml,ALT levels inunits/liter.
Capacityto return topretreatment steady-statelevels in
and ALT levels were determined at days 0, 7, and 14, and
subsequently every14days.For the virus decline as measured
from the decay during the first week of treatment, we obtain
u = 0.56 (a-=0.18, n =67) whichcorresponds to a Ti/2 of
1.2days. Average plasmavirusproductionis about 3 x 1012
(o-= 5 x 1012, n =57) particles per day.For the cellulardecay
rate (determined by comparingvirusproduction at day0 and
28)we obtain a wide distribution with anaverageofa = 0.053
per day (va=0.067, n =46) correspondingto aT/12of 13days.
There is, however, only a weak (not significant) correlation
between a and ALT levels in thesepatients, probablybecause
the estimate of a is problematic in some patients, which is
because viral measurements are often below detection limit
and viral increase aftertherapyis determined from virus titer
at days 28 and 42.
It islikelythat HBV infects andreplicatesat different rates
in a number of celltypes (16, 17).Therefore the estimated viral
productionrates and turnover rates of infected cells have to be
interpretedasaveragevalues.Similarly,the rate ofproduction
ofviralparticlesandHBeAgfrom an infected cellmay depend
on the number of cccDNA molecules of HBV in the nucleus
of an infected cell. During drugtreatment the cccDNAcopy
numberperinfected cellmay decline, which could lead to less
viral andHBeAg production independentof death of infected
cells. Therefore the decline of viral production and HBeAg
could overestimate the actual rate ofclearance ofinfected cells
and rather reflect the decay of cccDNA. But for practical
purposes the most important figure is the decay ofpotential
virus "production units" during treatment, independent of
whether this reflects cell death or decay of viral cccDNA.
However, the observed correlation between ALT and the
death rate of infected cells (as estimated by HBeAg decline)
argues in favor of clearance of infected cells as the major
mechanism. Patients with high ALT levels appear to clear
virus-producing units faster.
A half-life of 10daysfor infected, virus-producing hepato-
cytes impliesthat -7% of this cellpopulationis lostper day.
In a chronic HBV infection, between 5% and 40% of all
hepatocytescan be infected andproducevirus(18). Therefore,
between 0.3% and 3% of allhepatocytes are killed and must
bereplenished every dayto maintain a stable liver cell mass.
Since the liver contains -2 x 1011hepatocytes (19),this comes
to 109 cellsper day. This enormous activityof cell death and
regeneration islikelyto be amajor driving force fordevelop-
ment ofhepatocellular carcinoma (17, 20).
Our data provide an interesting comparison with HIV
dynamics (Table 1). In HIV infections, most patients have a
turnover rate of infected cells of -2 days and free virus is
cleared faster than this (21-24). In HBV infections, decay of
plasmavirus occurs with a half-life of
generallyseem to have noantibody againstfree virus. Inter-
estingly, there is a much wider distribution of half-lives of
virus-producingcells in HBV-infected patients ranging from
Table 1. HBV versus HIVdynamics
AcomparisonofHBV and HIV in vivodynamics.Both viruses have
arapidturnover and a massiveproductionofplasmavirus.Perhapsthe
mostimportantdifference is in the half-life ofvirus-producing cells,
which is much shorter for HIV. The HIV data are from refs. 21, 22,
2 X 1011
Mvedical Sciences: Nowak et al.
Medical Sciences: Nowak et al.
about 10 to 100 days. HBV is believed to be largely noncyto-
pathic,and therefore the turnover rates of infected cells can be
due to different anticellular immune responses. HIV, on the
other hand, canprobablykill an infected cell within a fewdays,
and the rather uniform turnover rate ofproductivelyinfected
cells could be theconsequenceof atight strugglebetween viral
cytopathicityand the strong cytotoxic T-lymphocyte response
found in most HIV patients. The large turnover of infected
CD4 cells in HIV infection ['109 CD4 cells are estimated to
be killed bythe virus and regenerated by the immune system
every day (21, 22)] is matched by an equivalent number of
hepatocytes in HBV infection. The total amount of plasma
virus production is larger for HBV; on average, -109 HIV
particles are generated every day comparedwith -101 HBV
particles.Thus chronic HBV infectionemerges also as arapid
dynamic processwith vast amounts of virus and infected cells
produced and killed every day.
Withrespectto accumulation ofgenetic diversityandescape
from drug treatment and immune responses, the relevant
figureis the viralgeneration time, which islargelydetermined
by the turnover rate of virus-infected cells and is therefore
much shorter in HIV. Another important factor is that the
genome lengthofHBV isonly -3200bp comparedto
bpfor HIV and thatmultiple overlapping readingframesmay
imposemore constraints againstvariation on HBV than HIV.
While there is rapid emergence of drug-resistant strains in
HIV (21, 25), we do not find any indication of resistance in
HBV; in our studies HBV virus loads do not increase aslong
as the drug is given.
Treatment of chronic HBV infections with lamivudine leads
to a rapid and sustained decline of plasma virus levels, but
clinical benefit with a reduced risk of cirrhosis and develop-
ment of liver cancer will greatly depend on the decline of
infected cells (26-28).Inpatientswhere infected cells decline
with a half-life of 10days,treatment for 1yearcouldpotentially
reduce the number of infected cells to -10-l
value (with a 100% effective drug). Eradication of the virus
infection depends on whether the efficacy of the drug is
sufficiently high to reduce the basic reproductiveratio of the
virus belowunity [in analogytoepidemiological theory (29)].
Inpatientswith an infected cell half-life of 100days,1yearof
treatment could reduce the number of infected cells to -8%
of its initial value. Thus lamivudine could be used over a
prolonged period as single-agent therapy or to reduce the
number of infected cells before immunotherapy designed to
eradicate infected cells. Immunotherapy without antiviral
treatment could be problematic because of the very large
number of infected liver cells in the typicalHBV carrier. The
quantitative understandingofHBVdynamicsderived here will
make it possible to devise optimal treatment strategies for
of its initial
We are indebted to S. Schalm, D. Tyrell, J. Main, J. Fevery, F.
Nevens, D. Mann, and K. Tanikawa forallowingus to use thehepatitis
B marker data from their patients on which our analysis is based.
Abraham Junior Research Fellow of Keble College.
is a Wellcome Trust Senior Research Fellow and E.P.
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