Modeling rotavirus strain dynamics in developed
countries to understand the potential impact of
vaccination on genotype distributions
Virginia E. Pitzera,b,1, Manish M. Patelc, Ben A. Lopmanc, Cécile Viboudb, Umesh D. Parasharc, and
Bryan T. Grenfella,b,d
aDepartment of Ecology and Evolutionary Biology anddWoodrow Wilson School of Public and International Affairs, Princeton University, Princeton, NJ 08544;
bFogarty International Center, National Institutes of Health, Bethesda, MD 20892; andcEpidemiology Branch, Division of Viral Diseases, National Center
for Immunization and Respiratory Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333
Edited by Simon A. Levin, Princeton University, Princeton, NJ, and approved October 21, 2011 (received for review June 29, 2011)
Understanding how immunity shapes the dynamics of multistrain
pathogens is essential in determining the selective pressures
imposed by vaccines. There is currently much interest in elucidating
the strain dynamics of rotavirus to determine whether vaccination
may lead to the replacement of vaccine-type strains. In developed
countries, G1P strains constitute the majority of rotavirus infec-
tions most years, but occasionally other genotypes dominate for
model to examine the interaction of five common rotavirus geno-
types. We explored a range of estimates for the relative strength of
homotypic vs. heterotypic immunity and compared model predic-
tions against observed genotype patterns from six countries. We
thenincorporatedvaccinationinthe model toexamine its impacton
rotavirus incidence and the distribution of strains. Our model can
explain the coexistence and cyclical pattern in the distribution of
genotypes observed in most developed countries. The predicted
frequency of cycling depends on the relative strength of homotypic
vs. heterotypic immunity. Vaccination that provides strong protec-
tion against G1 and weaker protection against other strains will
whereas a vaccine that provides equally strong immunity against all
strains may promote the continued predominance of G1. Overall,
however, disease incidence is expected to be substantially reduced
under both scenarios and remain below prevaccination levels de-
spite the possible emergence of new strains. Better understanding
of homotypic vs. heterotypic immunity, both natural and vaccine-
induced, will be critical in predicting the impact of vaccination.
mathematical modeling|transmission dynamics|strain replacement
shaping the epidemiological and evolutionary patterns of infec-
tious diseases (1). Models for the transmission dynamics of mul-
tistrain pathogens have helped elucidate the mechanisms behind
empirical patterns, including multiannual oscillations in the in-
cidence of influenza (2–4) and dengue cases (5–10), antigenic drift
within influenza subtypes (11–14), and cyclical patterns in the
predominance of different strains of influenza (3, 15), respiratory
syncytial virus (16), dengue (5–10), malaria (17), and cholera (18).
Vaccines that elicit a stronger immune response to specific strains
may impact the distribution of genotypes in unforeseen ways,
which inturnmayaffect overalldiseaseincidence. The responseof
multistrain pathogens to selective pressures imposed by vaccines is
a concern for many newly introduced vaccines, including human
papillomavirus, pneumococcal, and rotavirus vaccines (15, 19, 20).
Rotavirus is a major cause of severe gastroenteritis in both
humans and animals (21). More than half a million deaths each
year are attributed to rotavirus, most occurring in children <5 y
of age (22). Models for the transmission dynamics have aided our
understanding of the important factors driving epidemic patterns
of rotavirus diarrhea in the community (23). These models can
ifferences in the strength of immunity and cross-immunity
among strains are thought to play an important role in
be used to estimate the expected direct and indirect effects of
rotavirus vaccines (23–27) and have generated predictions that
agree with early observations of the impact of vaccination in the
United States (23). However, heretofore all models for the
transmission dynamics of rotavirus have ignored any complexity
relating to the different strains causing infections.
There are seven rotavirus groups (A–G), but the majority of
human disease is caused by rotavirus A (21). Group A rotavirus
strains can be differentiated both molecularly and serologically
according to their VP7 and VP4 surface proteins into G and P
types (21). Historically, four common rotavirus genotypes (G1P
, G2P, G3P, and G4P) have cocirculated along with
several less common genotypes (28). In developed countries, G1
strains constitute the majority of infections in most years, but
occasionally other genotypes dominate for reasons that are not
well understood. Over the past 2 decades, G9 strains emerged
and spread across the globe and are now considered to be the
fourth most prevalent genotype (28, 29). Efforts to monitor the
distribution of genotypes in different countries have increased in
anticipation of the introduction of rotavirus vaccines.
Evidence from observational studies and vaccine trials indicates
that natural rotavirus infection and vaccination confer both
homotypic [i.e., against the genotype causing natural infection or
genotype(s) included in the vaccine] and heterotypic [i.e., against
genotypes other than the infecting genotype or genotype(s) in-
cluded in the vaccine] protection. However, the nature and
strength of protection may vary depending on the number of pre-
vious infections and/or type of vaccine (e.g., animal, reassortant, or
human strain), and even homotypic protection is incomplete.
Prospective cohort studies that have identified and typed sequen-
tial infections in infants suggest that second infections are more
infection, but second infections with the same genotype can occur
(30–34). Although first infections elicit a predominantly homo-
typic,serum-neutralizingantibody response, subsequentinfections
generally elicit a broader, cross-reactive response (35, 36), pro-
viding one rationale for administering multiple doses of vaccine.
Currently licensed rotavirus vaccines consist of a single live
attenuated human G1P strain (Rotarix; GlaxoSmithKline) or
a pentavalent human–bovine reassortant strain containing the
G1, G2, G3, G4, and P surface proteins (RotaTeq; Merck)
(22). Although both vaccines have demonstrated similar efficacy
in clinical trials, they differ with respect to the immunological
Author contributions: V.E.P., M.M.P., B.A.L., C.V., U.D.P., and B.T.G. designed research,
performed research, analyzed data, and wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1To whom correspondence should be addressed. E-mail: email@example.com.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
| November 29, 2011
| vol. 108
| no. 48
mechanisms underlying protection (SI Appendix). The relative
importance of the various mechanisms of immunity is not en-
tirely understood (37).
Vaccination could impact the distribution of rotavirus strains
by increasing selection pressure on certain genotypes, potentially
leading to decreased vaccine effectiveness (20). During vaccine
trials, small discrepancies in efficacy were noted; however, these
trials typically lacked sufficient power to detect significant dif-
ferences in vaccine efficacy against homotypic vs. heterotypic
strains. Although there is speculation that rotavirus vaccines may
be impacting strain distributions in countries with routine im-
munization, there are not yet enough data to establish robust
Given the importance of this question to the ultimate success
of rotavirus vaccination programs, we sought to extend our
model for the transmission dynamics of rotavirus to incorporate
the interaction of five strains (23). We compared observed pat-
terns of genotype cycling with those predicted by our model,
exploring a range of possible values for the strength of homotypic
vs. heterotypic immunity. We then incorporated vaccination into
the model to explore the potential impact of vaccines that offer
differential protection against circulating strains and considered
the consequences of the emergence of a new strain. We conclude
by setting these results in the context of pathogen strain dy-
namics in general.
Empirical Patterns. To better understand the prevaccination cy-
cling of rotavirus genotypes and calibrate our strain-specific
model, we analyzed published time series of annual genotype
distributions from six developed countries (43–49). Fourier
analysis suggests that the predominant rotavirus strains cycle
with periods (T) ranging from 3 to 11 y (Fig. 1). We found sig-
nificant signals between T = 6.1 and 11.6 y for G1–G4 strains in
Italy, G4 in Hungary, G3 in the United States and Australia, and
G9 in Spain (Fig. 1B). In all countries, G1 strains exhibited
strong cycles between T = 5.8 and 10.7 y, although some coun-
tries also exhibited significant signals at shorter periods (e.g., T =
2.8–3.2 y for G1 strains in Spain, the United States, and Japan
and T = 2.4–3.2 for G2 in Australia and G9 in the United
States). Wavelet analysis of genotype distributions in Melbourne,
Australia revealed similar periodicities but did not suggest any
strong temporal trends (SI Appendix).
Modeling Prevaccination Dynamics. We developed a mathematical
model for the transmission dynamics of rotavirus that incorpo-
rated the interaction of five different strains. These strains are
meant to represent the five predominant G-types circulating in
most populations (G1–G4 and G9). We assumed the fifth strain
emerged 5 y into our simulations, in line with the recent world-
wide emergence of G9 (28, 29). Our model was able to repro-
duce the major patterns of genotype predominance, coexistence,
and cycling observed in the prevaccination era. When immunity
against second infection with a homotypic strain was assumed to
be much stronger than immunity against heterotypic strains (Fig.
2A, upper left corner), the model predicted a quicker cycling of
the predominant genotype (T ≈ 3 y), whereas when there was
only slightly stronger protection against homotypic compared
with heterotypic strains, the predicted period of oscillations was
considerably greater (T ≈ 8 y). These oscillations were also pres-
ent in the incidence data and were sustained regardless of wheth-
er we accounted for seasonality in the transmission rate (SI
Appendix). When immunity against homotypic and heterotypic
strains was equal or near equal, there was no cycling of genotypes
(Fig. 2A, lower right corner).
It was necessary to assume that G1 strains were slightly more
transmissible than other genotypes to fully explain why G1 is the
predominant genotype in temperate countries (SI Appendix).
When we assumed that the relative transmissibility of G2–G4
and G9 strains was 90% that of G1 strains, the model predicted
that G1 strains accounted for 41–100% of severe diarrhea cases,
depending on the strength of homotypic and heterotypic immu-
nity (Fig. 2B). When homotypic and heterotypic immunity were
nearly equal, only G1 strains persisted in the population (Fig. 2B,
lower right corner); it is possible to demonstrate mathematically
that a second strain is not able to invade (SI Appendix).
Epidemiologic studies suggest that the relative risk of second
infection with any strain, regardless of genotype, is 0.62 (95%
confidence interval, 0.5–0.83) (34). We considered this to be a
lower bound for the relative risk of second infection with a het-
erotypic strain. Thus, for subsequent analyses, we examined the
model-predicted patterns assuming σhe= 0.65 and σho= 0.35.
This yields a predicted period of genotype oscillations of ≈6 y,
and G1 strains account for 73% of severe diarrhea cases, which is
consistent with the observed data (Fig. 1) (28). We performed
sensitivity analyses with other immunity parameters to account
for the shorter (≈3-y) period also observed, but overall con-
clusions were similar (SI Appendix).
When we allowed for the extinction and stochastic reintro-
duction of strains, we found that the rarer genotypes (G2–G4,
G9) occasionally faded out and did not reappear for a number of
years (Fig. 3A). Variability in the period of oscillations increased,
particularly for non-G1 strains.
Impact of Vaccination. Vaccination that provides strong protection
against G1 and weaker protection against other strains results in
a large decrease in the proportion of infections caused by G1
1985 1990 1995 2000
19901995 2000 2005
1997 2000 2003 2006 2009
% of typed strains
Normalized Fourier amplitude
1988 1990 1992 1994 1996
G1G2G3 G4 G9
notype distributions (percentage of typeable rotavirus-positive samples) for
G1–G4 and G9, as described in refs. 43–49. (B) Fourier analysis of cyclical
patterns for each of the five genotypes. Fourier amplitudes for each geno-
type are plotted on a log scale for periods ranging from 2 to 12 y. Asterisks
represent significant signals according to bootstrap analysis.
Analysis of genotype oscillations observed in six countries. (A) Ge-
| www.pnas.org/cgi/doi/10.1073/pnas.1110507108Pitzer et al.
(Fig. 3B). There is a corresponding increase in the proportion of
infections caused by other genotypes, and quicker cycling of the
predominant genotype; a different genotype caused the majority
of cases every 2 to 3 y. The quicker cycling is due to the as-
sumption that non-G1 strains are comparable in terms of
transmissibility, and hence there is more frequent replacement.
The periodicity of the individual genotypes actually increased, as
expected because vaccination is similar to a reduction in birth
rate (SI Appendix). It is possible that G1 strains could be elimi-
nated at high coverage levels (Fig. 3C). However, the overall
incidence is substantially reduced despite the relative increase in
the proportion of infections caused by non-G1 strains.
If instead the vaccine is assumed to provide equally strong
protection against all five genotypes, vaccination is predicted to
lead to a slight increase in the proportion of infections caused by
G1 and a lengthening of the period of oscillations at intermediate
coverage levels, assuming G1 strains are slightly more trans-
missible (Fig. 3D). At higher coverage, the pattern of strain
oscillations becomes somewhat irregular as epidemics begin to
occur biennially and genotypes become more likely to fade out
during the epidemic troughs, but G1 remains the dominant ge-
notype (Fig. 3E).
Postvaccination Strain Emergence. The emergence of a new strain
after vaccination is predicted to have different effects depending
on the type of vaccine and whether it confers some or no pro-
tection against the emergent strain (SI Appendix, Table S2).
When vaccination is assumed to protect primarily against G1 and
provide weaker protection against all other strains including the
new strain (scenario 1), the new strain is expected to take a few
years to become established in the population, at which time it
causes a normal-sized epidemic (similar to postvaccination in-
cidence) and proceeds to cycle along with the other genotypes
(Fig. 4A). If the vaccine provides no protection against the
emergent strain (scenario 2), the new strain may cause an epi-
demic when it first emerges that is similar in size or slightly larger
than the average prevaccination epidemic; but after ≈3 y, in-
cidence is expected to decrease to slightly below prevaccination
levels (Fig. 4B). At intermediate coverage levels, only the new
strain and one other genotype (typically G1) are maintained in
the population, and these genotypes cycle every 4–6 y.
Relative risk of infection with homotypic strain (σho)
Relative risk of infection with heterotypic strain (σhe)
Period of strain oscillations
Proportion of cases due to G1
heterotypic immunity. The colorbars indicate (A) the dominant period of
oscillations for G1 strains (as indicated by the maximum Fourier amplitude)
and (B) the mean proportion of severe diarrhea cases due to G1 strains over
an 80-y period, for relative risks of second infection with homotypic strains
ranging from 0.01 to 0.5 (and relative infectiousness ranging from 0.1 to 0.5)
and relative risks of second infection with heterotypic strains ranging from
0.5 to 1.0 (with corresponding relative infectiousness).
Model-predicted patterns for different strengths of homotypic and
0510 15 20 25 30
Annual genotype distributions
Mean genotype distributions
0510 15 20 25 30
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0510 15 20 25 30
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0510 15 20 25 30
of severe rotavirus diarrhea. The proportion of cases in a given
year attributable to each genotype (Left), the weekly incidence
of severe rotavirus diarrhea (Center), and the mean genotype
situations: (A) prevaccination, (B) 50% coverage with a vaccine
that provides strong protection against G1 and weaker pro-
tection against other genotypes, (C) 80% coverage with such a
vaccine, (D) 50% coverage with a vaccine that provides strong
protection against all genotypes, and (E) 80% coverage with
such a vaccine. Vaccination is introduced in year 10 in B–E. The
results represent single realizations of a model allowing for
fadeout and stochastic reintroduction of genotypes.
Model-predicted genotype distributions and incidence
Pitzer et al.PNAS
| November 29, 2011
| vol. 108
| no. 48
When vaccination is assumed to provide strong protection
against G1–G4 and weak protection against the emergent strain
(scenario 3), the new strain again may take up to a few years to
become established and does not lead to an abnormally large
may lead to the extinction of other less-transmissible genotypes
(G2–G4); the new strain is predicted to cycle along with G1, with
T ≈ 8 y. If vaccination provides strong protection against G1-G4
and no protection against the emergent strain (scenario 4), the
new strain could lead to a large epidemic when it is first in-
troduced, with a peak incidence greater than prevaccination epi-
demics (Fig. 4D). The size of the epidemic will depend on when
such a strain emerges (SI Appendix). The new strain is expected to
become dominant in the population, whereas incidence is ex-
pected to stabilize at slightly below prevaccination levels.
Models for the transmission dynamics of rotavirus have provided
key insights into the epidemiology and impact of vaccination for
this important diarrheal pathogen (23–27). However, the models
developed thus far have not accounted for the different geno-
types that cocirculate in the population. Theory stemming from
multistrain models for various pathogens suggests that cross-
immunity can lead to cyclical patterns in incidence and the dis-
tribution of strains (e.g., refs. 2, 3, 7, 17, and 18). However, most
of these models assume that homotypic immunity is complete
and lifelong. Including the interaction of multiple strains of ro-
tavirus while accounting for the incomplete nature of immunity
makes the model considerably more complicated, and there are
only limited data on which to base assumptions about important
parameters, such as the strength of homotypic vs. heterotypic
immunity. Nevertheless, we are able to make some qualitatively
robust inferences that help explain the observed patterns of ge-
notype coexistence and cycling. We then use the model to ex-
plore the potential impact of vaccination on genotype patterns,
as well as scenarios in which a new strain emerges that partially
or fully escapes vaccine protection.
Understanding Observed Genotype Cycling. By examining fluctua-
tions in genotype distributions from six countries (43–49), we
found evidence of 3- to 11-y cycles in the predominant strains.
An interepidemic period of ≈5 y in the monthly incidence of
rotavirus hospitalizations with G1–G4 strains in Melbourne,
Australia has been previously noted (50, 51). The observed
variability in the dominant periods of oscillations is likely due to
the inherent stochasticity resulting from occasional fadeouts of
strains, the short length of available time-series data relative to
observed multiannual periodicities, and potential differences in
transmission dynamics among countries.
The cycling of rotavirus genotypes can be understood in terms
of the build-up of population-level immunity to the prevailing
strain. During the period in which G1 strains predominate, the
proportion of infants who have been infected with G1 but have
yet to experience a second infection gradually increases. These
individuals are less susceptible to a second infection with a G1
strain than they are to infection with a heterotypic strain. Thus,
even though G1 strains are more prevalent in the population at
that time (and may be slightly more transmissible among com-
pletely naïve individuals), the rarer genotypes gain a fitness ad-
vantage owing to their increased ability to infect those with
homotypic immunity to G1. The stronger homotypic immunity is
relative to heterotypic immunity, the quicker the cycling is
expected to occur, because it will take less time for the rarer
genotypes to gain a fitness advantage at the population level.
The rarer genotypes are able to infect both completely sus-
ceptible infants as well as slightly older individuals who have
experienced only one previous infection. As a result, the average
age of cases is expected to increase when there is a change in the
predominant strain (SI Appendix, Fig. S6). Indeed, it has been
noted that there was a slight shift in the age distribution of ro-
tavirus patients toward a broader spectrum of age groups after
changes in the predominant strain (52).
Although G1P strains represent >70% of clinical isolates in
North America, Europe, and Australia, countries in South
America, Asia, and Africa tend to be characterized by a greater
diversity of strains (28). Furthermore, cyclical variations in the
predominant genotypes may be more frequent in such countries.
G2 strains were found to be dominant or codominant with G1
every 3 to 4 y in South Africa (53). The higher birth rates typical
of such countries may help explain these patterns (SI Appendix).
It is not necessary to invoke molecular changes that alter the
fitness of the virus to explain the appearance and disappearance
of subdominant strains. Evidence argues against such changes
occurring. For example, it has been noted that closely related
strains can persist over multiple seasons, and that greater genetic
diversity can exist among strains belonging to a single G-type
circulating in the same year than strains belonging to that same
G-type reemerging 12–15 y later (43, 54). It seems unlikely that
such strains lose then regain some “fitness factor” during the
intervening years. The build-up of population-level homotypic
immunity is a more parsimonious explanation for the cycling of
strains both between and within G-types.
Additional Complexities in Modeling the Impact of Vaccination. Our
modeling approach provides a substantial advance over previous
efforts for rotavirus in that it considers up to five cocirculating
genotypes. However, residual complexities remain. For example,
G2P strains share neither the VP7 nor VP4 antigen with the
05 10 15 20 25 30
Annual genotype distributions
0510 15 20 25 30
Severe rotavirus cases
05 10 15 20 25 30
05 10 15 20 25 30
Number of hospitializations (per week)
05 10 15 20 25 30
0510 15 20 25 30
0510 15 20 25 30
0510 15 20 25 30
rotavirus diarrhea after the emergence of a new strain after vaccination. The
proportion of cases in a given year attributable to each genotype (Left) and
the weekly incidence of severe rotavirus diarrhea (Right) are plotted for 50%
coverage with (A) a vaccine that provides strong protection against G1 and
weaker heterotypic immunity to other genotypes, including the new strain
(scenario 1), (B) a vaccine targeting G1 that provides no immunity to the new
strain (scenario 2), (C) a vaccine that provides strong immunity against G1–
G4 but only weak immunity to the new strain (scenario 3), and (D) a vaccine
providing strong immunity against G1–G4 and no immunity to the new
strain (scenario 4). Vaccination is introduced in year 10, and the new strain is
introduced in year 15. The results represent single realizations of a model
allowing for fadeout and stochastic reintroduction of genotypes.
Model-predicted genotype distributions and incidence of severe
| www.pnas.org/cgi/doi/10.1073/pnas.1110507108Pitzer et al.
other common genotypes; therefore, heterotypic protection
scenarios we explored represent the breadth of possible immune
responses. Currently licensed vaccines probably fall at different
points along this spectrum, and we would need to make additional
assumptions to fully represent them (SI Appendix).
Our model predictions are for the most part consistent with early
observations, such as the predominance of G2P in Brazil and
Australian states using the Rotarix vaccine, and the continued
predominance of G1P in Australian states using RotaTeq (SI
Appendix) (38, 40, 41). However, other observations, such as out-
(39, 42), remain unexplained. The populations in different states/
countries are not isolated from one another, and it is difficult to
attribute short-term changes in genotype patterns to the effect of
vaccination in light of the natural cycling of genotypes and regional
Implications for Vaccine Escape. Despite possible changes in the
distribution of genotypes after vaccine introduction, our model
suggests overall disease incidence is expected to remain below
prevaccination levels if the vaccine provides at least some pro-
tection against emergent strains. This is to be expected if vacci-
nation mimics natural immunity. The emergence of G9 strains in
the late 1980s/early 1990s, as well as the more recent emergence
of G12 strains (20), did not result in unusually large epidemics.
The age distribution of cases caused by these strains has been
similar to that of the common genotypes (29), suggesting that
heterotypic immunity was effective at controlling these infections
and/or that newly emergent genotypes were slightly less trans-
missible. In the unlikely scenario that a new strain was to emerge
for which vaccination provided no immunity, our model suggests
it could lead to a large epidemic initially, particularly when
vaccination provides strong immunity against other strains.
Implications for Comparative Strain Dynamics. More generally, the
pattern of cyclical variation in the five common rotavirus geno-
types contrasts with the evolutionary dynamics exhibited by in-
fluenza A, for example, in which only two subtypes at most
cocirculate in the population, and gradual antigenic drift occurs
within subtypes. The antigenic drift of influenza strains occa-
sionally leads to changes that necessitate the updating of vac-
cines (55). Phylogenies of rotavirus VP7 genes do not exhibit
such strong patterns of drift, and the mutation rate of the virus is
lower because it is double-stranded (43, 44, 54). Thus, it seems
unlikely that the composition of rotavirus vaccines will need to
be updated as frequently as they are for influenza vaccines. Al-
though homotypic and heterotypic immunity likely play similar
roles in both systems and help explain between-subtype cycling,
the high transmissibility of rotavirus compared with influenza
[R0≈ 25 vs. 1.5 (23, 56)], along with slightly weaker homotypic
immunity and less reliance on metapopulation dynamics, may pro-
mote the coexistence of rotavirus strains rather than the sequential
replacement of strains within subtype (13).
Similar cyclical patterns are also evident among dengue sero-
types. Although cross-protective immunity may also account for
the cycling of dengue serotypes (5), most mathematical modeling
studies have attributed these patterns to antibody-dependent en-
hancement, whereby second infections with a different serotype
are assumed to be more transmissible and/or more likely to occur,
and immunity to the strain causing first infection is assumed to be
complete and lifelong (6–10). The potential for antibody-de-
pendent enhancement makes the development of vaccines for
dengue more complicated, because vaccination must provide
strong cross-protective immunity without increasing susceptibility
to severe disease (57).
Comparative studies that aid our understanding of the “phy-
lodynamics” (i.e., how features of the immunology and
epidemiology of pathogens affect their evolutionary trajectories,
and vice versa), and the implications for vaccination programs,
are an important avenue for future research (1).
Future Refinements and Data Needs. Our model is not designed to
capture all of the complexities of rotavirus strain variation (SI
Appendix) but nevertheless demonstrates some important con-
cepts. Mathematical modeling of rotavirus strain dynamics both
provides a tool by which we can gain a better understanding of why
the prevalent genotypes tendtocycle,andcanbeusedtospeculate
about how vaccination may impact genotypes distributions in the
future. Long-term surveillance of rotavirus genotype distributions
both before and after vaccine introduction is needed to validate
model predictions and gain a better understanding of the evolu-
rotavirus in developed countries; the findings may not be gener-
alizable to developing countries, where strain diversity is greater
and the protection from natural infection seems to differ (28, 30).
More epidemiological studies in birthcohorts are neededtoobtain
better estimates of the protection conferred by first infection with
one genotype against subsequent infection (symptomatic or
asymptomatic) with homotypic and heterotypic strains. Un-
derstanding the nature of homotypic vs. heterotypic immunity, and
how this affects the interaction of rotavirus genotypes as well as
other multistrain pathogens, will be critical for understanding ob-
Analysis of Genotype Time Series. Observed genotype time series with at least
10 y of consecutive data were gathered from the published literature (43–49)
(SI Appendix). We used Fourier analysis to detect the dominant multiannual
periodicities with which the various genotypes cycled in six countries.
Bootstrap analysis was used to identify significant periods of oscillation; we
randomly permuted the time series 1,000 times to identify signals that were
significant at the 95% confidence level.
Model Description. We extended an existing model for the transmission dy-
namics of rotavirus (23) to include strain-specific infection compartments.
Details of the model are presented in SI Appendix. In short, we assumed that
susceptible individuals can experience a primary infection with one of five
strains, recover and are temporarily immune to infection with all strains,
then can be reinfected at a reduced rate with either a homotypic or het-
erotypic strain. After two infections, individuals are assumed to develop
strong heterotypic immunity to all strains (SI Appendix provides sensitivity
analysis). We assumed that the transmission rate and seasonality parameters
were similar to those estimated for a best-fit model for rotavirus hospital-
izations in the United States (23) and a birth rate of 15 live births per 1,000 in
a population of 1 million individuals.
There is limited information to parameterize differences in homotypic vs.
heterotypic immunity (30–34). Thus, we explored a range of assumptions. The
relative risk of second infection with a homotypic strain (σho) was varied from
0.01 (near-complete homotypic immunity) to 0.5, whereas the relative risk of
second infection with a heterotypic strain (σhe) was varied from 0.5 to 1 (no
heterotypic immunity). We assumed that the relative infectiousness of second
infections was reduced in proportion to the relative risk, with a minimum rela-
tive infectiousness of 0.1. We explored whether small differences in the trans-
missibility of various strains or weaker homotypic immunity against G1 strains
(due to immunologically distinct sublineages) can explain the predominance
of G1 in temperate countries (SI Appendix). Fourier analysis was used to de-
termine the period of oscillations in model-predicted genotype distributions.
We identified a range of immunity parameters consistent with the period of
oscillations and proportion of infections caused by G1 in the observed data.
Modeling Vaccination. We examined the effect of two different vaccines
aG1strain (i.e.,strong immunitytoG1and weaker heterotypic immunitytoall
introduction at coverage levels of 50% and 80%. We also examined the
Pitzer et al.PNAS
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| vol. 108
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equilibrium distribution of strains averaged over a 20-y period 10 y after vac-
We allowed for the local extinction of strains when there was <0.5 primary
infection with a given strain to incorporate stochastic effects. Strains were
reintroduced into the population at a mean rate of one imported primary in-
fection per year; we varied this rate seasonally from a maximum of 1.5 intro-
ductions per year occurring at the same time as the peak in the transmission
rate to 0.5 introductions per year occurring during the nadir of transmission.
For both types of vaccine, we explored the effect of introducing the fifth
strain 5 y after vaccine introduction. The new strain was assumed to be 90%
as transmissible as G1 (equivalent to G2–G4). Under scenarios 1 and 3, we
assumed that the vaccine provided weak heterotypic immunity to the
newly emergent strain, whereas under scenarios 2 and 4, we assumed it
conferred no immunity to the new strain (SI Appendix, Table S2). Again,
we examined the dynamics over a 20-y period after vaccine introduction at
ACKNOWLEDGMENTS. This work was supported by National Institutes of
Health Grant R01 GM083983-01, the Bill and Melinda Gates Foundation, and
the Research and Policy for Infectious Disease Dynamics (RAPIDD) program of
the Science and Technology Directorate, Department of Homeland Security,
and the Fogarty International Center, National Institutes of Health (V.E.P and
B.G.). The findings and conclusions in this report are those of the authors and
do not necessarily represent the views of the Centers for Disease Control and
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