Infectivity versus fatality of SARS-CoV-2 mutations and influenza

Abstract

Objectives
Due to the spread of the Omicron variant, many countries have experienced COVID-19 case numbers unseen since the start of the pandemic. We aimed to compare the epidemiological characteristics of Omicron with prior variants and different strains of influenza, to provide context for public health responses.

Methods
We developed transmission models for SARS-CoV-2 variants as well as influenza, in which transmission, death, and vaccination rates were taken to be time-varying. We fit our model based on publicly available data in South Africa, the United States and Canada. We used this model to evaluate the relative transmissibility and mortality of Omicron compared to previous variants and influenza.

Results
We find that Omicron is more transmissible and less fatal than both seasonal and 2009 H1N1 influenza, as well as the Delta variant; these characteristics make Omicron epidemiologically more similar to influenza than it is to Delta. We estimate that as of February 7, 2022, booster doses have prevented 4.29×10^7 and 1.14×10^6 Omicron infections in the United States and Canada, respectively.

Conclusions
Our findings indicate that the high infectivity of Omicron will keep COVID-19 endemic, similarly to influenza. However, due to Omicron's lower fatality rate, our work suggests that human populations living with SARS-CoV-2 is most likely.

Full text

International Journal of Infectious Diseases 121 (2022) 195–202
Contents lists available at ScienceDirect
International Journal of Infectious Diseases
journal homepage: www.elsevier.com/locate/ijid
Infectivity versus fatality of SARS-CoV-2 mutations and influenza
Ling Xue
a
, Shuanglin Jing
a
, Kai Zhang
a
, Russell Milne
b
, Hao Wang
c , ∗
a
College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang, 150 0 01, China
b
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
c
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
a r t i c l e i n f o
Article history:
Received 18 March 2022
Revised 3 May 2022
Accepted 11 May 2022
Keywo rds:
Death rate
Effective reproduction number
Influenza
Omicron variant
Transmission rate
a b s t r a c t
Objectives: Because of the spread of the Omicron variant, many countries have experienced COVID-19
case numbers unseen since the start of the pandemic. We aimed to compare the epidemiological charac-
teristics of Omicron with previous variants and different strains of influenza to provide context for public
health responses.
Methods: We developed transmission models for SARS-CoV-2 variants and influenza, in which transmis-
sion, death, and vaccination rates were taken to be time-varying. We fit our model based on publicly
available data in South Africa, the United States, and Canada. We used this model to evaluate the relative
transmissibility and mortality of Omicron compared with previous variants and influenza.
Results: We found that Omicron is more transmissible and less fatal than both seasonal and 2009 H1N1
influenza and the Delta variant; these characteristics make Omicron epidemiologically more similar to
influenza than it is to Delta. We estimate that as of February 7, 2022, booster doses have prevented
4 . 29 ×10
7
and 1 . 14 ×10
6
Omicron infections in the United States and Canada, respectively.
Conclusion: Our findings indicate that the high infectivity of Omicron will keep COVID-19 endemic, sim-
ilar to influenza. However, because of Omicron’s lower fatality rate, our work suggests that human popu-
lations living with SARS-CoV-2 are most likely.
©2022 The Author(s). Published by Elsevier Ltd on behalf of International Society for Infectious
Diseases.
This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Introduction
On January 30, 2020, the World Health Organization (WHO) de-
clared COVID-19, which is caused by SARS-CoV-2, to be a public
health emergency ( World Health Organization, 2021c ). The ongoing
COVID-19 pandemic presents great threats to public health and sig-
nificant challenges to global economic development. As of February
20, 2022, the COVID-19 epidemic has caused more than 422 mil-
lion confirmed cases worldwide and a number of confirmed deaths
approaching 5.8 million ( World Health Organization, 2021a ). The
rapid mutation rate of the COVID-19 virus is also an important rea-
son for its great and long-lasting impact ( Yu et al., 2022 ): the suc-
cessive emergence of SARS-CoV-2 variants has caused a worldwide
multi-wave epidemic of COVID-19. In November 2021, the Omicron
variant (B.1.1.529) was first discovered in Gauteng, South Africa;
its swift spread led to the fourth wave of the COVID-19 pandemic
( Maslo et al., 2022 ; Planas et al., 2022 ).
∗Corresponding author: Hao Wang, Department of Mathematical and Statistical
Sciences, Universi ty of Alberta, Edmonton, Alberta T6G 2G1, Canada.
E-mail address: hao8@ualberta.ca (H. Wang) .
In the first 2 months after its discovery, the Omicron vari-
ant was identified in 110 countries across all six WHO regions
( Worl d Health Organization, 2021b ), and its infection rate has been
identified as being significantly faster than that of the Delta vari-
ant ( Wei et al., 2021 ; World Health Organization, 2021b ). As a
result of its fast spread, Omicron has come under intense study
( Cameroni et al., 2022 ; Cao et al., 2022 ; Cele et al., 2022 ; Liu et al.,
2022 ; Planas et al., 2022 ). Using high-throughput yeast display
screening, Cao et al. (2022) found that mutations present in Omi-
cron allowed it to escape from more than 85% of tested neu-
tralizing antibodies targeting its receptor-binding domain. Further-
more, Liu et al. (2022) found that Omicron is markedly resis-
tant to neutralization by serum not only from convalescent pa-
tients but also from individuals vaccinated with one of four widely
used COVID-19 vaccines (Pfizer, Moderna, J & J, and AstraZeneca).
Planas et al. (2022) found that Omicron often escapes from mono-
clonal and vaccine-elicited antibodies. However, their results also
included that antibodies generated by a recent booster vaccine
dose could neutralize Omicron ( Planas et al., 2022 ), albeit less ef-
fectively than other SARS-CoV-2 variants.
https://doi.org/10.1016/j.ijid.2022.05.031
1201-9712/© 2022 The Author(s). Published by Elsevier Ltd on behalf of International Society for Infectious Diseases. This is an open access article under the CC BY license
(
http://creativecommons.org/licenses/by/4.0/ )

L. Xue, S. Jing, K. Zhang et al. International Journal of Infectious Diseases 121 (2022) 195–202
Mathematical models can be used to understand the dynamics
of SARS-CoV-2 variants and help inform effective control strate-
gies, and many modeling studies have hence been performed to
make projections about the spread of these variants ( Liu and Rock-
löv, 2021 ; Yu et al., 2022 ). In a literature review, Liu and Rock-
löv (2021) found that estimates of Delta’s basic reproductive num-
ber ranged from 3.2 to 8, with a mean of 5.08, much higher than
that of the ancestral strain. Yu et al. (2022) used mathematical
models to estimate the relative transmissibility of Omicron using
variant proportion data in South Africa, finding that it is more
transmissible than Delta by a factor of approximately 3.8. Similarly,
Chen et al. (2022) found that Omicron is more transmissible than
Delta by a factor of 2.8 using an AI model. However, as the Omi-
cron variant is still new, our understanding of its infectivity and
fatality, and how these compare to other variants, is still evolv-
ing. Additionally, to the best of our knowledge, the question of
how the epidemiological properties of Omicron compare to those
of other fast-spreading viruses such as influenza has not yet been
addressed. To evaluate the properties of the Omicron variant, we
develop a mathematical model in which transmission, death, and
vaccination rates are all time-varying.
We fit our model using the numbers of new confirmed cases of
the Delta and Omicron variants, and all other variants in aggregate
(e.g., Beta, Gamma, Epsilon), in South Africa, the United States, and
Canada, and the number of individuals who have been fully vac-
cinated and who have received booster doses in those countries.
After this, we computed the transmission rate, death rate, and ef-
fective reproduction number of Delta, Omicron, and the other vari-
ants in each study jurisdiction. We also computed these statistics
for seasonal influenza and the 2009 strain of H1N1 influenza in
the United States and Canada by fitting case and death data to an-
other model (see Supporting Information Appendix). The epidemic
curves produced by our model fit the data very well, indicating
that our model captures the dynamics of the COVID-19 virus vari-
ants.
Materials and Methods
Data collection and analysis
To understand the impact of the SARS-CoV-2 variants on the
spread of the COVID-19 epidemic, we collected data on the pro-
portions of all SARS-CoV-2 infections that each of the variants ac-
counted for ( Our Worl d in Data, 2021 ). These data were reported
every 2 weeks from May 18, 2020, to February 7, 2022, in South
Africa, the United States, and Canada (Figure A1). We also collected
daily numbers of new confirmed cases and new deaths ( Centers for
Disease Control and Prevention, 2021 ; Our World in Data, 2021 )
and the number of fully vaccinated individuals, broken down into
those with and without booster doses ( Mathieu et al., 2021 ). We
used the relative prevalence of the SARS-CoV-2 variants to calcu-
late the daily numbers of new confirmed cases infected by Delta,
Omicron, and all other variants in our study countries. Similarly,
we calculated the daily number of new deaths in the study coun-
tries from Delta, Omicron, and all other variants by scaling total
COVID-19 deaths by the proportions of each SARS-CoV-2 variant
from 2 weeks before.
Model formulation
To mimic the spread of COVID-19, we constructed a disease
transmission model with vaccination. The total population (de-
noted by N) is divided into eight classes, namely S(t) , V
f
(t) , V
b
(t) ,
E(t) , A (t) , I(t) , R (t) , and D (t) , representing the numbers of individ-
uals who were (1) susceptible; (2) fully vaccinated, without having
received booster doses; (3) fully vaccinated, with booster doses;
(4) exposed; (5) infectious (asymptomatic); (6) infectious (symp-
tomatic); (7) recovered; and (8) dead of the infection, respectively.
The baseline infection probability among susceptible and vacci-
nated individuals is defined as
λ(
t
)
=
β(
t
) (
θE
(
t
)
+ δA
(
t
)
+ I
(
t
) )
N
,
where β(t) denotes the transmission rate, E(t) /N, A (t) /N, and
I(t) /Nare the probabilities of randomly encountering infected in-
dividuals in compartments E(t) , A (t) , and I(t) , respectively, and δ
and θrepresent the probabilities of transmission in asymptomatic
and exposed individuals, respectively. Susceptible and vaccinated
individuals who have encountered SARS-CoV-2 become exposed at
the rates λ(t) , ηf
λ(t) , and ηb
λ(t) , where 1 −ηf
and 1 −ηb
denote
the reduction in susceptibility to infection conferred by a com-
pleted vaccine series and a full vaccine series plus a booster dose,
respectively. Susceptible individuals transfer to the fully vaccinated
and recovered classes by vaccination at the rates ( 1 −q
f
) p
f
(t) S(t)
and q
f
p
f
(t) S(t) , respectively, where q
f
is the probability of com-
plete protection from COVID-19 after full vaccination, and p
f
(t)
denotes the rate of vaccine series completion. q
b
and p
b
(t) are
the analogous values for individuals receiving a booster dose. Ex-
posed individuals can become asymptomatic and symptomatic in-
fected individuals at the rates ρσE(t) and ( 1 −ρ) σE(t) , respec-
tively, where ρdenotes the proportion of infected individuals who
are asymptomatic and 1 /σdenotes the mean length of COVID-19
incubation period. Eventually, all cases in A (t) and I(t) will either
recover or die at the transition rates γA
and γI
, which are the re-
ciprocals of asymptomatic and symptomatic infection periods, re-
spectively. The death rate of asymptomatic infected individuals is
extremely low, so we only considered the death rate of symp-
tomatic individuals, μ(t) γI
, where μ(t) denotes their probability
of death. Our model is given by
⎧
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
d S
(
t
)
d t
= −λ(
t
)
S
(
t
)
−p
f
(
t
)
S
(
t
)
,
d V
f
(
t
)
d t
=
1 −q
f
p
f
(
t
)
S
(
t
)
−ηf
λ(
t
)
V
f
(
t
)
−p
b
(
t
)
V
f
(
t
)
,
d V
b
(
t
)
d t
=
(
1 −q
b
)
p
b
(
t
)
V
f
(
t
)
−ηb
λ(
t
)
V
b
(
t
)
,
d E
(
t
)
d t
= λ(
t
)
S
(
t
)
+ ηf
V
f
(
t
)
+ ηb
V
b
(
t
)
−σE
(
t
)
,
d A
(
t
)
d t
= ρσE
(
t
)
−γA
A
(
t
)
,
d I
(
t
)
d t
=
(
1 −ρ)
σE
(
t
)
−γI
I
(
t
)
,
d R
(
t
)
d t
= q
f
p
f
(
t
)
S
(
t
)
+ q
b
p
b
(
t
)
V
f
(
t
)
+ γA
A
(
t
)
+
(
1 −μ(
t
) )
γI
I
(
t
)
,
d D
(
t
)
d t
= μ(
t
)
γI
I
(
t
)
.
(1)
The model time step is 1 day. p
f
(t) , p
b
(t) , μ(t) , and β(t) are
all time-varying parameters, which were dynamically fitted using
an Markov Chain Monte Carlo (MCMC) method ( Haario et al., 2001 ,
2006 ). All parameters are listed in Table 1 ; model parametrization
is detailed in the Supporting Information Appendix.
According to the next generation matrix approach ( van den
Driessche and Watmough, 2002 ), the effective reproduction num-
ber, R
e
(t) , can be expressed as
R
e
(
t
)
=
S
(
t
)
+ ηf
V
f
(
t
)
+ ηb
V
b
(
t
)
N β(
t
)
θ
σ+
β(
t
) (
1 −ρ)
γI
+
β(
t
)
ρδ
γA , (2)
incorporating the daily numbers of new cases generated by ex-
posed, symptomatic, and asymptomatic individuals. The basic re-
production number is commonly used to measure transmission po-
tential at the beginning of an epidemic ( Diekmann et al., 199 0 ).
However, transmission potential varies over the course of an out-
break, and it can be measured at any time by the effective repro-
duction number.
Results
Infectivity
For each SARS-CoV-2 variant, we estimated its transmission
rates in South Africa, the United States, and Canada based on
196

L. Xue, S. Jing, K. Zhang et al. International Journal of Infectious Diseases 121 (2022) 195–202
Tabl e 1
The parameter description of Model (1).
Parameters Description (units) Value Source
1 /σMean duration of COVID-19’s incubation period (day) 5.2 Li et al. (2020)
δProbability of transmission for asymptomatic infected
individuals (dimensionless)
0.55 Li et al. (2020)
Hao et al. (2020)
θProbability of transmission for exposed individuals
(dimensionless)
0.55 Li et al. (2020)
Hao et al. (2020)
ρProportion of infected individuals who are asymptomatic
(dimensionless)
60% Qiu (2020)
1 / γA Infectious period of asymptomatic individuals (day) 8 Maier and Brockmann (2020)
1 / γI Infectious period of symptomatic individuals (day) 14 Kumar et al. (2021)
1 −ηf
Protection against infection generated by a full vaccine
series, without booster doses (dimensionless)
80% or 20% Ye et al. (2022) , AHIR (2021) ,
Ontario (2021)
1 −ηb
Protection against infection generated by receiving a
booster dose (dimensionless)
80% or 70% Ye et al. (2022)
National Health Service (2022)
q
f
Probability that an individual will be completely
protected from COVID-19 after two doses of vaccine
(dimensionless)
0 estimated
q
b
Probability that an individual will be completely
protected from COVID-19 after booster doses of vaccine
(dimensionless)
0 Estimated
μ(t) Probability of deaths among symptomatic individuals
(dimensionless)
see Figures 1 , B2, B3 Estimated
p
f
(t) Proportion of fully vaccinated individuals who have not
received any booster doses (
da y
−1
)
see Supporting
Information
MCMC
p
b
(t) Proportion of fully vaccinated individuals who have
received booster doses (
da y
−1
)
see Supporting
Information
MCMC
β(t) Transmission rate ( da y
−1
) see Figures 1 , B2, B3 MCMC
NTota l population (South Africa)
Tota l population (United States)
Tota l population (Canada)
55700000
329500000
38000000
Worl d Health Organization (2021e)
data from the time periods in each country during which it first
emerged. We performed our analysis with both raw case numbers
( Figures 1 , B2, and B3) and 7-day averaged data (Figures E10, E11,
and E12). The two cubic splines that we used for transmission rate
(based on the raw and smoothed data) were highly similar for all
variants and countries ( Figures 2 , E13, and E14), showing the ro-
bustness of our methods.
In South Africa, the average transmission rate of the Omicron
variant was 0.4201 from November 1, 2021, to December 26, 2021
( Figure 1 A). For Delta, this was 0.1264 from March 9, 2021, to May
2, 2021 ( Figure 1 C), and for all other variants, it was 0.1629 from
March 5, 2020, to April 28, 2020 ( Figure 1 E). We estimate that
Omicron’s transmission rate is 3.3 times that of Delta and 2.6 times
that of the other variants in South Africa; these values are consis-
tent with previous studies ( Chen et al., 2022 ; Yu et al., 2022 ).
In the United States, Omicron’s average transmission rate was
0.6794 from November 21, 2021, to December 26, 2021 (Figure
B2A). This was 0.1981 for Delta from May 2, 2021, to June 6, 2021
(Figure B2C), and 0.3299 for other variants from January 23, 2020,
to February 27, 2020 (Figure B2E). In the United States, the trans-
mission rate of Omicron is higher than that of Delta and other vari-
ants by factors of 3.4 and 2.1, respectively.
In Canada, Omicron had an average transmission rate of 0.5735
from November 15 , 2021, to December 26, 2021 (Figure B3A),
whereas that of Delta was 0.0373 from February 23, 2021, to April
5, 2021 (Figure B3C), and the rate for the other variants was 0.1693
from January 26, 2020, to March 7, 2020 (Figure B3E). Omicron’s
transmission rate in Canada is 15. 4 times and 3.4 times that of
Delta and other variants, respectively.
Fatality
We estimated the lethality of the different variants by using
their average death rates. For Delta, Omicron, and other variants
in aggregate, these are 0.0020, 8 . 741 ×10
−4
, and 0.0022 in South
Africa ( Figures 1 B, D, F), respectively. There, Delta’s death rate is
2.3 times that of Omicron, whereas the death rate of the variants
other than Delta and Omicron is 1.1 times and 2.5 times those of
Delta and Omicron, respectively. In the United States, we found
that the death rates of Delta, Omicron, and the other variants are,
in order, 8 . 282 ×10
−4
, 1 . 758 ×10
−4
, and 0.0019 (Figures B2B, D,
F). There, the death rate of Delta is 4.7 times that of Omicron, and
the death rate of the other variants is 10. 8 times that of Omicron.
In Canada, the death rate of Delta is 5 . 816 ×10
−4
, whereas this is
1 . 887 ×10
−4 for Omicron and 0.0014 for the other variants (Fig-
ures B3B, D, F). Delta’s death rate in Canada is higher than that of
Omicron by a factor of 3.1; for the other variants, this factor is 7.4.
The previously mentioned analysis shows that Delta and especially
Omicron have lower death rates than previous variants.
Effective reproduction number
To calculate the effective reproduction numbers for each SARS-
CoV-2 variant, we substituted the estimated parameters into
Eq. (2) ( Figure 3 ). We subsequently found the average effective re-
production numbers for the considered regions, considering the
time from the date the first case was reported until 1 month
later. We found that for Omicron, the average effective reproduc-
tion numbers in South Africa, the United States, and Canada are
6.39, 6.34, and 5.44, respectively. For Delta, these are 0.78, 1.50,
and 0.31, and for variants other than Omicron and Delta, these are
1.2 4 , 3.74, and 1.5 7. Thus, Omicron’s average effective reproduction
number is 8.2 times that of Delta in South Africa, 4.2 times that of
Delta in the United States, and 17.5 times that of Delta in Canada.
Likewise, the average effective reproduction number for Omicron
was 5.2, 1.7, and 3.5 times that of variants other than Omicron and
Delta in those three countries.
Booster dose effectiveness
We additionally determined the protection rate of booster doses
against infection by Omicron in the United States and Canada, as
shown in Figure 4 (Because the distribution of booster doses in
South Africa began on January 17, 2022, we did not consider the
197

L. Xue, S. Jing, K. Zhang et al. International Journal of Infectious Diseases 121 (2022) 195–202
Figure 1. Model fitting based on data for COVID-19 cases and deaths in South Africa. Panels A, C, and E show the fitting of the transmission rates for variants other than
Delta and Omicron, the Delta varian t, and the Omicron variant, respectively, based on daily numbers of new confirmed cases of these variants. Panels B, D, and F show
the fitting of the variants’ death rates (in the same order), based on daily numbers of new deaths because of each variant. The transmission rates were taken to be cubic
spline functions, with numbers of nodes
n
βequal to 13 for variants other than Delta and Omicron, seven for Delta, and six for Omicron. In each subplot, the red curve
represents the mean simulated number of cases or deaths, and the blue curve represents the transmission or death rate. The 95% PI and CI are plotted in pink and magenta,
respectively. CI, confidence interval; PI, prediction interval.
effectiveness of booster doses on Omicron there.). As of February
7, 2022, we found that vaccination has reduced the number of in-
fected people by 4 . 29 ×10
7 and 1 . 14 ×10
6 in the United States
and Canada, respectively, and reduced the number of deaths by
1 . 32 ×10
5 and 4 . 17 ×10
3 in those countries. These results im-
ply that with 70% protection against Omicron (see Table 1 ), booster
doses of currently available vaccines can significantly reduce mor-
tality.
COVID-19 and seasonal influenza
To estimate the transmission and death rates of seasonal in-
fluenza, we collected weekly numbers of new confirmed cases and
deaths from August 6, 2017, to December 22, 2019, in the United
States and Canada. We used these to fit a seasonal influenza trans-
mission model (see Supporting Information Appendix). Our param-
eter fitting, using the same methods as for model (1), is shown
in Figures D6 and D7. We then compared these rates with the
corresponding ones for Omicron over the full course of its out-
break to capture transmission dynamics in all outbreak phases. We
chose a longer interval to model dynamics over because seasonal
influenza is not an emerging disease. In the United States, the av-
erage transmission rates of seasonal influenza and Omicron were
0.120 and 0.407, respectively; the rate for seasonal influenza ranged
from 0.041 to 0.202, whereas that of Omicron ranged from 0.0418
to 1.06 4. The average death rate of seasonal influenza in the United
States was 0.0064 (ranging from 0.0013 to 0.0202), whereas that of
Omicron was 1 . 758 ×10
−4 (ranging from 0 to 5 . 987 ×10
−4
). In
Canada, seasonal influenza and Omicron had average transmission
rates of 0.158 (ranging from 0.0183 to 0.266) and 0.360 (ranging
from 0.0817 to 0.838), respectively. The average death rates of sea-
sonal influenza and Omicron were 0.0019 and 1 . 887 ×10
−4
, re-
spectively, with ranges from 0 to 0.0816 for seasonal influenza and
from 0 to 0.0018 for Omicron. These results indicate that Omicron’s
profile (high transmissibility, low mortality) is a more exaggerated
version of seasonal influenza, suggesting that Omicron outbreaks
may be more like those of seasonal influenza than those of Delta.
COVID-19 and 2009 H1N1 influenza
To compare the transmission and death rates of the 2009 strain
of H1N1 influenza with those of Omicron, we collected daily num-
bers of cumulative confirmed cases and deaths of H1N1 from April
23, 2009, to July 6, 2009, in the United States and Canada. We used
the same model for H1N1 as for seasonal influenza; the parameter
fitting is shown in Figures D8 and D9 (see Supporting Information
Appendix). We subsequently found the average transmission and
death rates for the considered regions, calculated using the rates
from the date the first case was reported until 2 months later. In
the United States, the average transmission rate of H1N1 was 0.347
(ranging from 0.0783 to 0.590), and that of Omicron over a simi-
lar time period of approximately 2 months from the first detec-
tion was 0.509 (ranging from 0.142 to 1.06 4). The average death
rates of H1N1 and Omicron were 0.0020 and 1 . 372 ×10
−4
, re-
spectively, with ranges from 1 . 751 ×10
−4
to 0.0125 for H1N1 and
from 0 to 5 . 553 ×10
−4
for Omicron. In Canada, the average trans-
198

L. Xue, S. Jing, K. Zhang et al. International Journal of Infectious Diseases 121 (2022) 195–202
Figure 2. Estimation of transmission and death rates in South Africa using actual data versus a 7-day rolling average. Panels A, C, and E show transmission rates for variants
besides Delta and Omicron, the Delta variant, and the Omicron variant, respectively. Panels B, D, and F show the variants’ death rates, in the same order.
mission rates of H1N1 and Omicron were 0.320 and 0.470, respec-
tively; the rate for H1N1 ranged from 0.0903 to 0.751, whereas that
for Omicron ranged from 0.0893 to 0.8383. The average death rate
of H1N1 in Canada is 6 . 257 ×10
−4 (ranging from 1 . 424 ×10
−4
to 0.0024); for Omicron, this is 8 . 522 ×10
−5 (ranging from 0 to
5 . 372 ×10
−4
). Hence, compared with those of H1N1, Omicron’s
average transmission rate was 46% higher in the United States and
47% higher in Canada, whereas Omicron’s average death rate was
97% lower in the United States and 90% lower in Canada, results
analogous to how Omicron is more transmissible and less deadly
than seasonal influenza.
Discussion
The successive emergence of COVID-19 virus variants has
caused multiple COVID-19 outbreak waves across the world. In Oc-
tober 2020, the Delta variant (B.1.617.2) was discovered in Maha-
rashtra, India ( del Rio et al., 2021 ), which was a driving factor in
the second wave of COVID-19 in that country. In November 2021,
the Omicron variant (B.1.1.529) was first discovered in Gauteng,
South Africa, and quickly spread to other countries ( Maslo et al.,
2022 ; Planas et al., 2022 ). This led to the fourth wave of the
COVID-19 pandemic: Omicron replaced Delta as the dominant
strain after 8 weeks in South Africa and later accounted for more
than 90% of all cases after 8 and 10 weeks of circulation in the
United States and Canada, respectively.
To understand the SARS-CoV-2 variants’ epidemiological prop-
erties, we developed a model describing their dynamics, featuring
time-varying rates of transmission, death, and vaccination. We cre-
ated an inverse method to estimate the time-varying death rate
of the COVID-19 virus variants, which greatly simplifies the com-
plexity of parameter estimation. Using this method, we found that
the transmission rate of Omicron is 3.3 times that of Delta in
South Africa, and the death rate of Delta is 2.3 times that of Omi-
cron there. Correspondingly, these numbers are 3.4 and 4.7 in the
United States and 15.4 and 3.1 in Canada. This makes it clear that
Omicron is more infective but less lethal than Delta. We also found
that with a complete vaccine series plus a booster dose provid-
ing 70% protection against Omicron, vaccination has reduced the
number of infected people by 4 . 29 ×10
7 and 1 . 14 ×10
6 in the
United States and Canada, respectively.
During the COVID-19 pandemic, comparisons with seasonal in-
fluenza have been frequently made by public officials ( Faust and
del Rio, 2020 ), and influenza has been used as a point of refer-
ence for clinical studies of patients with COVID-19 ( Brehm et al.,
2021 ; Xie et al., 2020 ). Previous variants of SARS-CoV-2 were char-
acterized by higher mortality than seasonal influenza, even after
accounting for the underreporting of influenza deaths ( Faust and
del Rio, 2020 ). However, our results indicate that the Omicron
199

L. Xue, S. Jing, K. Zhang et al. International Journal of Infectious Diseases 121 (2022) 195–202
Figure 3. Effective reproduction number for variants of SARS-CoV-2. Each row of graphs shows different variants within a given country (from top to bottom: South Africa,
the United States, and Canada). The columns show results for particular variants (from left to right: varia nts other than Delta and Omicron, the Delta varian t, the Omicron
variant). The 95% CIs are plotted in magenta. CI, confidence interval; SARS-CoV-2, severe acute respiratory syndrome coronavirus 2.
variant has a lower death rate than seasonal influenza, the op-
posite of other SARS-CoV-2 variants. Similarly, the COVID-19 pan-
demic was compared with H1N1 in 2009, only a few months af-
ter the beginning of the former ( Jhaveri, 2020 ). Clinically, the two
diseases result in similar immune responses ( Morris et al., 2021 ),
and many computed tomography imaging features are common to
both ( Yin et al., 2020 ). In contrast to early variants of SARS-CoV-
2, which were observed to have higher mortality rates than 2009
H1N1 influenza ( da Costa et al., 2020 ), we found Omicron to be
less deadly than that strain. We also found Omicron to be more
transmissible than the tested varieties of influenza. Our results in-
dicate that although Omicron must be taken seriously because of
its high infectivity, its low fatality suggests that it can serve as a
less dangerous replacement for other SARS-CoV-2 strains, outcom-
peting them but causing less damage.
We found that the Omicron variant is epidemiologically more
similar to influenza than previous SARS-CoV-2 variants; this is ev-
ident by its unique mutations, which confer upon it a different
evolutionary strategy ( Du et al., 2022 ). Hence, we predict that
methods for combating Omicron based on previous public health
responses to seasonal influenza will be effective. Earlier in the
COVID-19 pandemic, it was found that nonpharmaceutical inter-
ventions to suppress COVID-19 in China also had the effect of sup-
pressing seasonal influenza cases because the two diseases share
similar transmission methods ( Lei et al., 2020 ). Seasonal influenza
is characterized by wintertime outbreak peaks and yearly variabil-
ity in epidemiological characteristics ( Chowell et al., 2008 ). So far,
the COVID-19 pandemic has also exhibited these features, with
new SARS-CoV-2 variants emerging at least once per year. Further
variants in Omicron’s lineage have been observed ( Desingu et al.,
2022 ), and because of Omicron’s ubiquity, the next dominant vari-
ant may be one of its descendants. Therefore, as the future of the
COVID-19 pandemic may revolve around managing viruses with
similar characteristics as Omicron, applying strategies originally
designed for seasonal influenza will prove useful.
Our study still has several limitations. First, because the num-
bers of recovered and asymptomatic infected individuals are not
publicly available yet, our simulations only used incidence data,
death cases, and the number of fully vaccinated individuals. Sec-
ond, the numbers of new confirmed cases and deaths for each vari-
ant are intertwined with the reported data and hard to disentangle
from it. We used the proportions of cases caused by each SARS-
CoV-2 variant to calculate these numbers. Third, we used model
(1) to fit three SARS-CoV-2 variants under the assumption that an
individual can be simultaneously infected with different variants.
Fourth, we did not consider human mobility and imported cases
from overseas or the role of environmental factors; these will be
studied when such data become available.
Declaration of Competing Interest
The authors have no conflicts of interest to declare.
Funding source
LX is funded by the National Natural Science Foundation of
China 12171116 and Fundamental Research Funds for the Cen-
tral Universities of China 3072020CFT2402. HW is partially sup-
ported by NSERC Individual Discovery Grant RGPIN-2020-03911
and NSERC Discovery Accelerator Supplement Award RGPAS-2020-
0 0 090.
200

L. Xue, S. Jing, K. Zhang et al. International Journal of Infectious Diseases 121 (2022) 195–202
Figure 4. Effectiveness of vaccines against the Omicron variant in South Africa, the United States, and Canada. The black boxes, red curves, and green curves represent the
number of reported cases or deaths, simulated mean under the scenario where booster doses are administered at rates fit to current data, and simulated mean under the
scenario where no booster doses are administered, respectively.
Ethical approval statement
This article does not contain any studies involving animals or
humans performed by any authors.
Author contributions
HW designed research; all authors conceived the work; SJ, KZ,
and HW performed research; all authors analyzed data; LX, SJ, and
KZ wrote the initial draft; all authors edited the manuscript.
Supplementary materials
Supplementary material associated with this article can be
found, in the online version, at doi: 10.1016/j.ijid.2022.05.031 .
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202

Supporting Information (SI):
1
Infectivity versus fatality of SARS-CoV-2 mutations and influenza
2
Ling Xue1, Shuanglin Jing1, Kai Zhang1, Russell Milne2, Hao Wang3,
3
1 College of Mathematical Sciences, Harbin Engineering University, Harbin, Heilongjiang,
4
150001, China
5
2 Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1,
6
Canada
7
3 Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta
8
T6G 2R3, Canada
9
* Corresponding author. Email: hao8@ualberta.ca.
10
11

A. Changes in the relative proportions of SARS-CoV-2 variants over time
12
Data on the proportions of all COVID-19 cases caused by the Delta variant, the Omicron variant,
13
and all other variants in our three study countries (South Africa, the United States, and Canada)
14
is shown in Fig. A.1. (Note that these reports reflect sequenced cases, and hence the actual
15
relative prevalences of each of the variants may be different.) We used this data while
16
constructing our model, to estimate the number of cases and deaths that each variant was
17
responsible for at any given point in time. We can obtain from this data that it took 20 weeks
18
from its first reported cases for the Delta variant to account for more than 90% of all cases in
19
South Africa, while it only took eight weeks for the Omicron variant to do the same there (Fig.
20
A.1(A)). Similar patterns were visible in the United States and Canada (Figs. A.1(B), (C)). In
21
those two countries, the Omicron variant had risen above 90% of all cases as of the latest data
22
used in our analysis, and needed much less time to do so after its initial detection in each country
23
compared to the Delta variant. These results indicate that the Omicron variant spreads more
24
quickly than, and can hence outcompete, the Delta variant.
25

26
Figure A.1: The proportions of all SARS-CoV-2 infections caused by the Delta and Omicron
27
variants, as well as all other SARS-CoV-2 variants in aggregate. (A) South Africa. (B) the
28
United States. (C) Canada.
29
30
B. Parameter estimation
31
To quantify the dynamics of the COVID-19 virus variants in South Africa, the United States, and
32
Canada, we fit Model (1) (see Materials and Methods section) to the numbers of new confirmed
33
cases, fully vaccinated individuals, and administered booster doses in those countries. In the
34
simulations, we assume that the total population was constant within each country, as shown in
35

Table 1 in the Materials and Methods section; we took the total populations of our study
36
countries from World Health Organization data (WHO 2021e). We also assume that the initial
37
numbers of symptomatic and asymptomatic infected individuals are  and
38
, respectively, and the initial number of exposed individuals was assumed to be
39
the same as the number of initially infected individuals. We take the initial number of susceptible
40
individuals to be .  and  can be deduced from the number
41
of fully vaccinated individuals without and with booster doses, respectively. Since the incubation
42
period of COVID-19 is around 5.2 days (Q. Li et al. 2020), we take the rate  governing
43
individuals becoming infectious following exposure to be . Moreover, we assume that the
44
average recovery periods for symptomatic and asymptomatic infected individuals are 14 and 8
45
days (Maier and Brockmann 2020, Kumar et al. 2021), respectively, leading to  and
46
 per day. Around 30%-60% of people infected with due to COVID-19 are
47
asymptomatic or only have mild symptoms; within this subpopulation, SARS-CoV-2
48
transmissibility is lower, but still significant (Qiu 2020). Thus, we assume that the probability of
49
an infected individual being asymptomatic is , and we set  (R. Li et al.
50
2020, Hao et al. 2020) due to lower transmissibility among both exposed and asymptomatic
51
infected individuals. Using reports from the Africa Health Research Institute (AHRI 2021) and
52
the Ontario Dashboard (Ontario 2021), we assume that the protection rates against infection by
53
Omicron and other strains after full vaccination are 20% and 80% (Ye et al. 2022), respectively,
54
i.e.  or . We also assume that the protection rates against infection by
55
Omicron and other strains after a booster vaccine dose are 70% and 80% (Ye et al. 2022, NHS
56
2022), respectively, i.e.  or .
57
58

The transmission rate, , is assumed to be a piecewise cubic spline function with  nodes
59
(Stone et al. 2020), i.e. we let . Similarly, the vaccination and booster dose
60
administration rates,  and , are assumed to be piecewise cubic spline functions with
61
 and  nodes, i.e.  and . In order to estimate the
62
time-varying mortality rate , we let  and  be the daily numbers of new confirmed
63
cases and new deaths, respectively. For our main results, we use raw daily data rather than 7-day
64
rolling averages, as the observed periodicity in COVID-19 data can be learned by forecasting
65
algorithms (Ramazi et al. 2021). However, to control for potential 7-day periodic signals in
66
upstream causes such as travel patterns (Edsberg Møllgaard et al. 2021) and health care provider
67
hours (Greene et al. 2021), we also perform the same analysis using 7-day averages of case and
68
death data. Next, we use splines and trigonometric functions to interpolate the observed data to
69
generate smooth curves for  and  (Kong et al. 2015, Pollicott et al. 2012). In keeping
70
with Model (1), we use the values of  and  as approximations of the
71
daily numbers of new confirmed cases and new deaths, respectively; in other words, we let
72
 and . Therefore, since  and  are known,
73
we obtain
74


Because 
, we have
75

