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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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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