SARS-CoV-2 coinfections:Implications for the second wave

Lubna Pinky∗,‡, Hana M. Dobrovolny †

∗Department of Pediatrics, University of Tennessee Health Science Center†Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX

Background

• The early part of the SARS-CoV-2 pandemiccoincided with circulation of other respiratoryviruses, such as influenza, and the second waveis expected to coincide with the upcoming in-fluenza season.

• Since SARS-CoV-2 is co-circulating withother respiratory viruses, viral coinfections arelikely to occur. However, in the initial phaseof the pandemic, clinicians noted fewer SARS-CoV-2 coinfections than were expected.

• We use mathematical models to investigatethe mechanism for the lack of coinfections andto investigate what that might mean for a sec-ond wave.

In-host coinfection model

In this model, the viruses interact via competi-tion for the resource of cells.

Target cells

Eclipse cells Infectious cells

Infectious cellsEclipse cells

Target cells :dT

dt= −β1TV1 − β2TV2

Eclipse cells :dEi

dt= βiTVi − kiEi

Infected cells :dIidt

= kiEi − δiIi

Virus :dVidt

= piIi − ciVi.

Viruses

We fit single virus models to parameter-ize the model for influenza (IAV), humanrhinovirus (hRV), respiratory syncytial virus(RSV), parainfluenza virus (PIV), and humanmetapneumovirus (hMPV).

0 10 20 30 40Time (d)

101

102

103

104

105

Vir

al l

oad

(co

pie

s/m

L)

SARS-CoV-2

0 2 4 6 8 10Days post infection (dpi)

10-2

100

102

104

106

108

Vir

al t

iter

(P

FU

/mL

)

Model resultExperimental data

IAV

0 2 4 6 8 10Days post infection (dpi)

10-2

100

102

104

106

Vir

al t

iter

(T

CID

50/m

l)

Model result Experimental data

hRV

0 2 4 6 8 10Days post infection (dpi)

10-2

100

102

104

106

Vir

al t

iter

(P

FU

/mL

)

Model resultExperimental data

RSV

0 2 4 6 8 10Days post infection (dpi)

10-2

100

102

104

106

108

Vir

al t

iter

(T

CID

50

/ml)

Model result Experimental data

PIV

0 2 4 6 8 10Days post infection (dpi)

10-2

100

102

104

Vir

al t

iter

(T

CID

50

/ml)

Model resultExperimental data

hMPV

SARS-CoV-2 coinfections

0 2 4 6 8 10 12 14Time (d)

100

102

104

106

108

Vir

al t

iter

CoV-2 single infection

IAV single infection

CoV-2 coinfectionIAV coinfection

0 2 4 6 8 10 12 14Time (d)

100

102

104

106

108

Vir

al t

iter

CoV-2 single infection

RSV single infection

CoV-2 coinfectionRSV coinfection

0 2 4 6 8 10 12 14Time (d)

100

102

104

106

108

Vir

al t

iter

CoV-2 single infection

hRV single infection

CoV-2 coinfectionhRV coinfection

0 2 4 6 8 10 12 14Time (d)

100

102

104

106

108

Vir

al t

iter

CoV-2 single infection

PIV single infection

CoV-2 coinfectionPIV coinfection

0 2 4 6 8 10 12 14Time (d)

100

102

104

106

108

Vir

al t

iter

CoV-2 single infection

hMPV single infection

CoV-2 coinfectionhMPV coinfection

SARS-CoV-2 infections are suppressed by otherrespiratory viruses.

Role of growth rate

Virus IAV RSV hRVGrowth rate (/d) 11.9 5.41 13.6

Virus PIV hMPV SARSGrowth rate (/d) 3.99 9.07 1.80

Viruses with higher growth rates infect cellsfaster than viruses with lower growth rate, leav-ing the slower virus with no cells to to infect.

Sequential infections

0 3 6 9 12 15 18 21 24 27 30Time (d)

10 1

102

105

108

Vira

l tite

r

IAV SARS-CoV-2

0 3 6 9 12 15 18 21 24 27 30Time (d)

10 1

102

105

108

Vira

l tite

r

RSV SARS-CoV-2

0 3 6 9 12 15 18 21 24 27 30Time (d)

10 1

102

105

108

Vira

l tite

r

HRV SARS-CoV-2

0 3 6 9 12 15 18 21 24 27 30Time (d)

10 1

102

105

108

Vira

l tite

r

PIV SARS-CoV-2

0 3 6 9 12 15 18 21 24 27 30Time (d)

10 1

102

105

108

Vira

l tite

r

HMPV SARS-CoV-2

Even if the second infection is initiated afterSARS-CoV-2, it can still suppress SARS-CoV-2.

Epidemiological model

If SARS-CoV-2 is so easily suppressed by otherrespiratory viruses, what might be the impli-cations for a second wave? We developed anepidemiological model where one virus preventscoinfection with the other.

(Susceptible)

(Infected with Flu) (Infected with CoV-2)

Recovered(from Flu)Susceptible(to CoV-2)

(Exposed to Flu)(Exposed to CoV-2)

(Recovered)

(Recovered from CoV-2Susceptible to Flu)

(Infected with Flu)(Infected with CoV-2)

(Coinfected)

k2

δ1

1k

2δ

k2 1k

δ12δ

3δ

(Exposed to CoV-2)(Exposed to Flu)

(Exposed to both)(Recovered from FluSusceptible to CoV-2)

(I +I + )1 3

(I +I + )1 3

S

E2E1

1I 2I

3I

E3

R

(I +I +E + )2 3 3

1k

1S(2)

2E(1) 1E(2)

S2(1)

I(2)1

I(1)2

I(2)1

I(2)1

(I +I + )1 3I(1)2

(I +I + )1 3 I(1)2ß1/N

ß1/N

(I +I +E + )2 3 3I(2)1 2ß /N

ß1/N

2ß /N ß1/N

I(2)1

Epidemiological parameters

Flu (H1N1) SARS-CoV-2βi, d−1 0.50 0.41ki, d−1 0.25 0.20δi, d−1 0.20 0.10δ3, d−1 0.1 or 0.01

Flu parameters from Gonzalez-Parra et al. (2015) Acta TropicaSARS-CoV-2 parameters from Anderson et al. (2020) The Lancet

Two virus epidemic

90 180 270 360 450Time (days)

02468

101214

Infe

cted

pop

ulat

ion

(log 1

0) FluCoV-2CoinfectedSingle infection: FluSingle infection: CoV-2

90 180 270 360 450Time (days)

02468

101214

Rec

over

ed in

fect

ed (l

og10

)

Recovered from Flu,infected with CoV-2Recovered from CoV-2,infected with Flu

90 180 270 360 450Time (days)

02468

101214

Infe

cted

pop

ulat

ion

(log 1

0) FluCoV-2CoinfectedSingle infection: FluSingle infection: CoV-2

90 180 270 360 450Time (days)

02468

101214

Rec

over

ed in

fect

ed (l

og10

)

Recovered from Flu,infected with CoV-2Recovered from CoV-2,infected with Flu

Influenza’s ability to block SARS-CoV-2 leadsto a delay in the SARS-CoV-2 epidemic.

Hospitalization

We looked at the total number of infected peopleas a proxy for possible hospitalization.

90 180 270 360 450Time (days)

02468

101214

Infe

cted

pop

ulat

ion

(log 1

0)

Absolute recovery rate=0.1 d 1

Total Flu and CoV-2infected with coinfectionTotal Flu and CoV-2infected without coinfection

90 180 270 360 450Time (days)

02468

101214

Infe

cted

pop

ulat

ion

(log 1

0)

Absolute recovery rate=0.01 d 1

Total Flu and CoV-2infected with coinfectionTotal Flu and CoV-2infected without coinfection

We find a double peak in the hospitalizations;the first caused by influenza patients, the sec-ond caused by SARS-CoV-2 patients.

Parameter sensitivity

We used partial rank correlation coefficient todetermine which parameters are most importantfor determining the course of the epidemic.

Total Hospitalization Time Between Peaks

Aside from the hospitalization rates (h1 and h2)total number of hospitalized patients is moststrongly determined by the infection rate of in-fluenza while the timing between peaks is deter-mined by both infection rates and the hospital-ization rate of influenza.

Conclusions

• Within the host, coinfecting viruses com-pete for the resource of cells.

• SARS-CoV-2 appears to have a lowerwithin host growth rate than other respi-ratory viruses and tends to be suppressedduring coinfections.

• At the population level, co-circulation ofinfluenza and SARS-CoV-2 leads to a tem-porary suppression of SARS-CoV-2 infec-tions. Once people have recovered frominfluenza, SARS-CoV-2 reappears.

• This results in a double peak in the num-ber of infected people — the first peakcaused by influenza, the second by SARS-CoV-2.