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Immuno-epidemiological life-history and thedynamics of SARS-CoV-2 over the next five years

Chadi M. Saad-Roy,1⇤ Caroline E. Wagner,2,3⇤

Rachel E. Baker,2,3 Sinead E. Morris,4 Jeremy Farrar5

Andrea L. Graham,2 Simon A. Levin,2

C. Jessica E. Metcalf,2,6 Bryan T. Grenfell2,6,7†

1Lewis-Sigler Institute for Integrative Genomics,Princeton University, Princeton NJ 08540, USA

2Department of Ecology and Evolutionary Biology,Princeton University, Princeton NJ 08544, USA

3Princeton Environmental Institute,Princeton University, Princeton NJ 08544, USA

4Department of Pathology and Cell Biology,Columbia University Medical Center, New York NY 10032, USA

5 The Wellcome Trust, London, UK6Princeton School of Public and International Affairs,

Princeton University, Princeton NJ 08544, USA7Fogarty International Center, National Institutes of Health, Bethesda MD 20892, USA,

⇤These authors contributed equally to this work†To whom correspondence should be addressed; E-mail: [email protected]

Uncertainty in the immune response to SARS-CoV-2 may have implications1

for future outbreaks. We use simple epidemiological models to explore esti-2

mates for the magnitude and timing of future Covid-19 cases given different3

impacts of the adaptive immune response to SARS-CoV-2 as well as its in-4

1

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https://doi.org/10.1101/2020.07.15.20154401


teraction with vaccines and nonpharmaceutical interventions. We find that5

variations in the immune response to primary SARS-CoV-2 infections and a6

potential vaccine can lead to dramatically different immunity landscapes and7

burdens of critically severe cases, ranging from sustained epidemics to near8

elimination. Our findings illustrate likely complexities in future Covid-19 dy-9

namics, and highlight the importance of immunological characterization be-10

yond the measurement of active infections for adequately characterizing the11

immune landscape generated by SARS-CoV-2 infections.12

Introduction13

The current Covid-19 pandemic caused by the novel SARS-CoV-2 betacoronavirus (�–CoV)14

has resulted in substantial morbidity and mortality, with over ten million confirmed cases world-15

wide at the time of writing. In order to curb viral transmission, non-pharmaceutical interven-16

tions (NPIs) including business and school closures, restrictions on movement, and total lock-17

downs have been implemented to various degrees around the world. Major efforts to develop18

effective vaccines and antivirals are ongoing.19

20

Understanding the future trajectory of this disease requires knowledge of the population-21

level landscape of immunity generated by the life histories of SARS-CoV-2 infection or vac-22

cination among individual hosts, particularly in the context of the acquisition, re-transmission,23

and clinical severity of secondary infections. The nature of acquired immune responses fol-24

lowing natural infection varies substantially among pathogens. At one end of this immune25

spectrum, natural infection with measles (1) or smallpox (2) virus results in lifelong protec-26

tion from the re-acquisition and re-transmission of secondary infections. Many other infections27

(e.g. influenza (3), RSV (4)) confer imperfect or transient clinical and transmission-blocking28

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immunity. Finally, phenomena such as antibody-dependent enhancement (ADE) associated29

with prior natural infection (e.g. dengue (5)) or a vaccine (e.g. RSV (6)) could result in more30

clinically severe secondary infections. Furthermore, the immunity conferred by vaccines to var-31

ious pathogens rarely provides complete protection against reinfection and/or disease (9), and32

this protection may be inferior to that acquired following natural infection (10). Nevertheless,33

imperfect vaccines that reduce both the clinical severity and transmissibility of subsequent in-34

fections (if they do occur) can still provide population-level disease protection (9, 11).35

36

In the case of SARS-CoV-2, the nature of the immune response following natural infection37

remains uncertain, although efforts to measure the kinetic adaptive immune response are on-38

going (12–16). One approach for bounding estimates for this immune response is to examine39

related viruses that also belong to the �–CoV genus. This genus comprises other viruses that40

cause severe infections in humans including the Middle East Respiratory Syndrome (MERS)41

and SARS-CoV-1 coronaviruses (7) as well as the seasonal coronaviruses HCoV-HKU1 and42

HCoV-OC43, which are the second leading causes of the common cold (7). While immunity to43

SARS-CoV-1 is believed to last up to 2-3 years (17, 18), serum antibody levels against HCoV-44

OC43 have been found to wane on the time-scale of a few months (19) to one year (20) likely45

due in part to a combination of antigenic evolution and low antigenic dose. HCoV-HKU1 and46

HCoV-OC43 are thought to cause repeated infections throughout life (21), though a significant47

biennial component in their dynamics implies at least some herd protection (7,8). Furthermore,48

although it is currently unclear whether ADE influences the pathogenesis of SARS-CoV-2, it has49

been hypothesized that severe Covid-19 cases may arise from the presence of non-neutralizing50

antibodies from prior coronavirus infections (22) following earlier proposals for related coron-51

aviruses (23–25). For example, one study found that a subset of reinfections with three endemic52

human coronaviruses (HCoV-NL63, HCoV-229E, and HCoV-OC43) showed enhanced viral53

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Figure 1: Schematic of the SIR(S) model with a flowchart depicting flows between immuneclasses. Here, SP denotes fully susceptible individuals; IP denotes individuals with primaryinfection that transmit at rate �; R denotes fully immune individuals (due to recovery fromeither primary or secondary infection), SS denotes individuals whose immunity has waned atrate � and are now susceptible again to infection, with relative susceptibility ✏; IS denotesindividuals with secondary infection that transmit at a reduced rate ↵�, and µ denotes the birthrate (see Methods). Illustrations and flowcharts of the limiting SIR and SIRS models are alsoshown (where individuals are either fully susceptible (S), infected (I), or fully immune (R)),along with a representative time series for the number of infections in each scenario. Thepopulation schematics were made through Biorender.com.

replication during the secondary infection (26). In addition to antibody-mediated immunity, T54

cell immunity increasingly appears to be an important component of the adaptive immune re-55

sponse to SARS-CoV-2; also there is evidence of T cell cross-reactivity between SARS-CoV-256

and these seasonal, endemic coronaviruses (15, 16).57

58

Various epidemiological models have been developed to capture this type of variation in im-59

mune responses on population-level infection dynamics. For instance, the well-known Susceptible-60

Infectious-Recovered (SIR) model is suitable for modeling the dynamics of perfectly-immunizing61

infections such as measles (27), while the Susceptible-Infectious-Recovered-Susceptible (SIRS)62

model captures the epidemiology of imperfectly immunizing infections such as influenza, in63

which individuals eventually return to a fully or substantially susceptible class following a finite64

period of immunity either due to waning memory or pathogen evolution (28). More complex65

compartmental models have also been developed to study infections characterized by interme-66

diate immune responses lying between these two extremes such as rotavirus (29) and respiratory67

syncytial virus (4).68

69

Here we adopt a generalization of these more nuanced models, the SIR(S) model (28) out-70

lined schematically in Figure 1 and Figure S1, to explore how the pandemic trajectory might71

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unfold for different assumptions regarding the nature of the adaptive immune response to SARS-72

CoV-2 infection. Since different adaptive immune responses may be associated with variations73

in the proportion of severe secondary cases, we also consider different scenarios for this fraction74

in order to estimate the future clinical burden of SARS-CoV-2 infections. The model assumes75

different infection and immune phenotypes depending on exposure history (see Methods for the76

full mathematical details). Specifically, it interpolates between the fully immunizing SIR model77

when immunity is lifelong and the imperfectly immunizing SIRS model through the degree of78

susceptibility to and transmissibility of secondary infections (quantified by the parameters ✏ and79

↵, respectively). As shown in the representative time series of Figure 1, the SIR model results in80

recurrent epidemics fueled by births following the pandemic peak, while the SIRS model results81

in shorter inter-epidemic periods due to the possibility of reinfection and the buffering of the82

fully susceptible birth cohort by partially immune individuals (28). We begin by characterizing83

the effect of temporal changes in the transmission rate brought about by climate and the adop-84

tion of NPIs on the predictions of the SIR(S) model under a range of immunity assumptions.85

Next, we examine the effect of a transmission-reducing vaccine of varying efficacy relative to86

natural immunity, thus altering the relative compositions of the various immune classes. Fi-87

nally, we estimate the post-pandemic immunity landscape and clinical case burden for different88

possible ‘futures’ shaped by the various aspects of SARS-CoV-2 biology as well as the presence89

or absence of these external drivers and interventions.90

91

Results and Discussion92

Seasonal transmission rates and the adoption of NPIs93

In practice, during the early stages of a pandemic, reductions in transmission are nearly entirely94

achieved through the adoption of NPIs such as mask-wearing or social distancing. To explore95

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the effect of the adoption of NPIs, we considered two different scenarios for timed reductions96

in the force of infection to 60% of its original value (in agreement with intermediate levels of97

social distancing in (7)). In Figures 2a - 2c, we plot the time series of primary and secondary98

infections assuming NYC climate-driven seasonality in transmission as well as single periods of99

NPI adoption lasting from weeks 16 to 67 (Figure 2a) or 16 to 55 (Figure 2b), and two shorter100

periods during weeks 16 to 55 and weeks 82 to 93 separated by normal interactions (Figure101

2c). The weekly reproduction numbers corresponding to these three scenarios are plotted in102

Figures S2d-S2f. Although these reproduction numbers are based on those obtained for the re-103

lated �-CoV HCoV-HKU1 and are in general lower than those estimated during the early stages104

of the Covid-19 pandemic (30), they may be more appropriate for considering the longer-term105

transmission dynamics, and our results are qualitatively robust to increasing these values for R0106

(results not shown).107

108

We find that decreases in the susceptibility to secondary infection ✏ can delay secondary109

peaks (compare individual time courses for different values of ✏ in Figures 2a–2c). However,110

delayed peaks may then be larger, due to susceptible accumulation and dynamical resonance.111

These non-monotonicities in the timing and size of secondary peaks also occur with climate-112

driven seasonal transmission in the absence of NPIs (see Supplementary Materials, Section113

S3.3). Importantly, the delay that social distancing may cause in the timing of the secondary114

peak can also allow for the accumulation of fully susceptible individuals. This is illustrated in115

the top panels of Figure 2d, where the full (�SP , red curve) and partial (✏�SS , green curve)116

effective population-level susceptibility corresponding to a reduction in susceptibility to sec-117

ondary infection by 50% (✏ = 0.5) (left) and with no reduction in susceptibility to secondary118

infection (✏ = 1) (right) for the social distancing scenario outlined in Figure 2c are shown. The119

corresponding fraction of primary (blue) and secondary (purple) cases are presented in the bot-120

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Figure 2: (a) to (c): Effect of NPI adoption on the time series of primary (solid lines) andsecondary (dashed lines) infections with a seasonal transmission rate derived from the climateof NYC with no lag between seasonality and epidemic onset. NPIs that reduces the transmissionrate to 60% of the estimated climate value are assumed to be adopted during weeks 16-67 in(a), weeks 16-55 in (b), and weeks 16-55 as well as 82-93 in (c). Colours denote individualtime courses for different values of ✏. (d) Time series of the force of infection arising fromsusceptibility (top row) and the fraction of the population that is infected (bottom row) for bothprimary and secondary infections, for ✏ = 0.5 (left column) and ✏ = 1 (right column) for theNPI scenario outlined in (c). (e) Time series of estimated number of severe infections for theNPI scenario defined in (c) for four different estimates of the fraction of severe cases duringprimary infections (xsev,p) and secondary infections (xsev,p) with ✏ = 0.5 (top row) and ✏ = 1(bottom row). These are xsev,p = 0.14, xsev,s = 0 (solid red line), xsev,p = 0.14, xsev,s = 0.07(dashed green line), xsev,p = 0.14, xsev,s = 0.14 (dashed-dotted blue line), and xsev,p = 0.14,xsev,s = 0.21 (shortdashed-longdashed purple line).

tom panels. As can be seen, when the secondary peak does occur, the decrease in susceptibility121

to secondary infection (✏ < 1) considered in the left panels results in a greater number of pri-122

mary infections during the second peak relative to the panels on the right where ✏ = 1.123

124

Finally, an essential part of the planning and management of future SARS-CoV-2 infections125

is the ability to characterize the magnitude and timing of severe cases requiring hospitaliza-126

tion. In Figure 2e we consider four different plausible scenarios for the fraction of severe127

secondary cases xsev,s (see Methods) based on the scenario depicted in Figure 2c and assum-128

ing 14% of primary cases are severe (31): no severe cases associated with secondary infection129

(xsev,s = 0, solid red line), a reduced number of severe cases with secondary infection rela-130

tive to primary infection (xsev,s = 0.07, dashed green line), comparable proportions of severe131

cases (xsev,s = 0.14, dashed-dotted blue line), and a greater proportion of severe cases with132

secondary infection (xsev,s = 0.21, shortdashed-longdashed purple line), possibly owing to133

phenomena such as ADE. When the assumed fraction of severe secondary infections is high,134

the fraction of the population with severe infections during secondary peaks exceeds that ob-135

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served during the primary peak (Figure 2e). As the proportion of secondary infections increases136

during the later stages of the pandemic, these findings stress that clinical epidemiological stud-137

ies of repeat infections will be critical for proper planning of healthcare systems.138

Vaccination139

The availability of an effective vaccine would be a key intervention against SARS-CoV-2, and140

numerous candidates are in development (32, 33). Intuitively, if the effective vaccination rate141

is sufficiently high, then vaccination herd immunity generated by a transmission-blocking vac-142

cine could control or eliminate the infection. However, this becomes harder to achieve when143

vaccinal and natural immunity is imperfect and secondary infections occur, or when logistical144

or other constraints limit vaccine deployment. Although it remains uncertain whether and when145

a vaccine will be available, we make the relatively optimistic assumption that a transmission-146

reducing vaccine begins to be introduced at tvax = 1.5 years. We also consider seasonal147

transmission rates as in Figure S3 and the adoption of NPIs according to the scenario described148

in Figure 2b. We assume that a constant proportion ⌫ ranging from 0% ⌫ 1% of the fully149

and partially susceptible populations (SP and SS) is effectively vaccinated every week and ac-150

quire transmission-blocking immunity for, on average, a period 1/�vax. For comparison, it was151

estimated that in response to the 2009 H1N1 pandemic, one or more doses of the monovalent152

vaccine were administered to 80.8 million vaccinees during October 2009 to May 2010 in the153

United States (34), which implies a rate of vaccination coverage of about 27% after a period154

of 8 months for persons aged at least 6 months in the USA, although rates between different155

nations varied (35). This crudely corresponds to a weekly vaccination rate of 1% (36). Finally,156

we assume that the immunity conferred from effective vaccination wanes at rate �vax which in157

general may differ from the waning rate of immunity from natural infection, �. The modified158

set of ordinary differential equations in this scenario corresponding to the flowchart in Figure159

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S11a is presented in the Methods.160

161

In Figure 3a we consider the long-term equilibrium infection burden (see Methods) fol-162

lowing vaccination at a weekly rate ⌫ for a variety of immunity assumptions. As expected, a163

reduction in the susceptibility to secondary infections (✏) results in a smaller number of infec-164

tions at steady state in the absence of vaccination. Further, both ✏ and the duration of vaccine165

immunity (1/�vax) affect the vaccination rate required to achieve a disease-free state at equi-166

librium. In the limit of fully immunizing primary infections and vaccines (✏ = 0), relatively167

low vaccination rates are required to achieve zero infections at steady state. However, as im-168

munity becomes more imperfect (larger ✏), increasingly high vaccination rates are required to169

eliminate infections particularly when the duration of vaccine immunity is short. This is further170

emphasized in Figure 3b, where the minimum vaccination rate ⌫ required to achieve a disease-171

free state at equilibrium (see Methods) is plotted as a function of ✏ for different values of the172

duration of vaccine immunity. Altogether, this illustrates that reductions in infection achievable173

through vaccination are inherently related to the efficacy of the vaccine and the nature of the174

adaptive immune response (37).175

176

We next explore the short-term dynamical effect of vaccination in Figures 3c-3f. In Figure177

S11b, the ratio of the total number of primary infections during years 1.5-5 inclusive (i.e. after178

the vaccine is introduced) relative to the zero vaccination case for different values of the vac-179

cination rate ⌫ and the duration of vaccine immunity 1/�vax is shown. Figure S11c shows the180

equivalent for secondary infections. The burden of primary infections decreases with increas-181

ing vaccination rate for a given value of vaccine immunity 1/�vax. However, for the shortest182

durations of vaccine immunity 1/�vax, the degree of achievable reductions in the number of183

secondary cases begins to saturate even for large vaccination rates. This saturation is due to the184

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Figure 3: (a) Total infected fraction of the population at equilibrium as a function of the vac-cination rate ⌫ for different values of the duration of vaccine immunity (1/�vax = 0.25 years:green line, 1/�vax = 0.5 years: red line, and 1/�vax = 1 year: blue line) and the susceptibilityto secondary infection (✏ = 0.5: solid line, ✏ = 0.7: dashed line, and ✏ = 1: dotted line).(b) Vaccination rate ⌫ required to achieve a disease-free state at equilibrium as a function of✏ for different values of the duration of vaccine immunity (1/�vax = 0.25 years: solid line,1/�vax = 0.5 years: dashed line, and 1/�vax = 1 year: dotted line). In (a) and (b) the relativetransmissibility of secondary infections and duration of natural immunity are taken to be ↵ = 1and 1/� = 1 year, respectively, and the transmission rate is derived from the mean value ofseasonal NYC-based weekly reproduction numbers (R0 = 1.75, see Methods and Figure S2c).(c)-(f): Time series of the various immune classes plotted for different values of the vaccinationrate ⌫. The top row ((c) and (e)) contains the time series of primary (solid lines) and secondary(dashed lines) infections, while the bottom row ((d) and (f)) contains the time series of the fullysusceptible (solid lines), immune (dashed lines), and partially immune (dotted lines) subpop-ulations. The duration of vaccine immunity is taken to be 1/�vax = 0.5 years (shorter thannatural immunity) in (c) and (d), and 1/�vax = 1 year (equal to natural immunity) in (e) and(f). The susceptibility to secondary infection, relative transmissibility of secondary infections,and duration of natural immunity are taken to be ✏ = 0.7, ↵ = 1, and 1/� = 1 year, respectively.Vaccination is introduced 1.5 years after the onset of the epidemic following a 40 week periodof social distancing during which the force of infection was reduced to 60% of its original valueduring weeks 16 to 55 (i.e. the scenario described in Figure 2b of the main text), and a seasonaltransmission rate derived from the climate of NYC with no lag is assumed.

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Figure 4: Time series of fraction of the population with severe cases Isev (top) and area plots ofthe fraction of the population comprising each immune class (bottom) over a five year time pe-riod under four different future scenarios. In all plots, the relative transmissibility of secondaryinfections is taken to be ↵ = 1, a seasonal transmission rate derived from the climate of NYCwith no lag is assumed, and a period of social distancing during which the force of infectionis reduced to 60% of its original value during weeks 16 to 55 (i.e. the scenario described inFigure 2b) is enforced. In (a) and (b), no vaccination occurs. (a) Corresponds to a more pes-simistic natural immunity scenario with ✏ = 0.7, 1/� = 0.5 years, and 21% of secondary casesbeing severe. (b) Corresponds to a more optimistic natural immunity scenario with ✏ = 0.5,1/� = 2 years, and 7% of secondary cases being severe. In (c) and (d), vaccination is intro-duced at a weekly rate of ⌫ = 1% at tvax = 1.5 years after the onset of the epidemic. (c)Corresponds to all the parameters in (b) along with vaccine immunity lasting 1/�vax = 0.25years, while (d) corresponds to all the same parameters as in (b) along with vaccine immunitylasting 1/�vax = 1 year.

rapid return of vaccinated individuals to the partially susceptible class if vaccine immunity is185

short-lived. Further, when the duration of vaccine immunity is very short, the total number of186

secondary cases can be higher when vaccination takes place for the particular model and param-187

eters considered. To further emphasize the dependence of the model results on the vaccination188

rate and duration of vaccine immunity, we present time courses of infections and immunity for189

different durations of vaccine immunity and vaccination rates in Figures 3c - 3f as well as Fig-190

ures S11d and S11e. In line with intuition, the model illustrates that both high vaccination rates191

and relatively long durations of vaccine-induced immunity are required to achieve the largest192

reductions in secondary infection burdens.193

194

Clinical case burden and immunity landscape for different possible futures195

Figure 4 is a synoptic view of the impact of vaccination and natural immunity in four different196

‘futures’ on the immune landscape and incidence of severe disease. In all four scenarios, we197

assume seasonal transmission (c.f. Figure S3) and social distancing according to the scenario198

depicted in Figure 2b. Figures 4a and 4b correspond to futures without vaccination, with Fig-199

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ure 4a illustrating a more pessimistic scenario of greater susceptibility to secondary infections200

(✏ = 0.7), a relatively short period of natural immunity (1/� = 0.5 years), and a greater pro-201

portion of severe cases with secondary infection possibly owing to phenomena such as ADE. In202

contrast, the more optimistic future of Figure 4b assumes reduced susceptibility to secondary203

infections (✏ = 0.5), a longer duration of natural immunity (1/� = 2 years), and a smaller204

proportion of severe cases with secondary infection. In both cases, the initial pandemic wave205

is the same, but in the more optimistic scenario (Figure 4b), natural immunity is longer lasting206

and consequently subsequent infection peaks are delayed. Furthermore, the reduction in sus-207

ceptibility to secondary infection (smaller ✏) in Figure 4b suppresses the later peaks dominated208

by secondary infections (Figure 4a) and substantially less depletion of fully susceptible indi-209

viduals occurs. In Figures 4c and 4d, these pessimistic and optimistic scenarios are translated210

into futures with vaccination, which is assumed to be introduced at a weekly rate of ⌫ = 1% at211

tvax = 1.5 years. The future described in Figure 4c assumes all the same outcomes as in Fig-212

ure 4a and incorporates vaccination with short-lived vaccine immunity (1/�vax = 0.25 years).213

The future presented in Figure 4d assumes all the same outcomes as in Figure 4b in addition to214

vaccine immunity lasting 1/�vax = 1 year.215

216

Figures 4c and 4d emphasize the important role that even an imperfect vaccine could have217

in SARS-CoV-2 dynamics and control (9, 11). With vaccination, subsequent peaks in clinically218

severe cases are substantially reduced, although in the pessimistic future later infection peaks219

dominated by secondary infections can still occur (Figure 4c). Furthermore, if a transmission-220

blocking vaccine confers a relatively long period of protection, and if we make optimistic as-221

sumptions regarding the nature of the adaptive immune response (Figure 4d), a sufficient pro-222

portion of fully susceptible individuals can be immunized, thus suppressing future outbreaks.223

These trends are qualitatively conserved for different vaccine deployment strategies, such as a224

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pulse of immunization at tvax = 1.5 years in which a fixed percentage of the fully and par-225

tially susceptible populations (SP and SS) are vaccinated (see Figure S12). However, without226

sustained immunization strategies, the waning of vaccine immunity results in less susceptible227

depletion over time, and larger future outbreaks relative to the scenarios presented in Figures228

4c and 4d. Overall, Figure 4 suggests that relying on the status of infection of an individual229

as the main observable during an ongoing epidemic is insufficient to characterize the complex230

immune landscape that is generated. Given the increasingly recognized importance of both T231

cell- (15, 16) and antibody-mediated (12–14) adaptive immune responses in the recovery from232

SARS-CoV-2 infection, it is very likely that more sophisticated methods including regular test-233

ing of serology and T cell immunity will be required (38).234

235

Conclusion236

We have examined how plausible variations in the natural immune response following SARS-237

CoV-2 infection as well as various external drivers and interventions may shape the longer-term238

clinical burden and immunity landscape to this disease. Here we summarize the key findings239

and complexities illustrated by this simple model along with caveats for their interpretation; a240

full summary of all caveats and future directions is given in Section S2.241

242

In locations where we expect substantial climatically-driven seasonal variation in transmis-243

sion, such as New York City, the model predicts that a reduction in susceptibility to secondary244

infection or a longer duration of immunity may lead to a larger secondary infection peak, and245

this peak may occur earlier when the duration of natural immunity is longer. In geographical246

areas with smaller annual fluctuations in climate, we find that this non-monotonic behaviour247

is increasingly suppressed, although these results are sensitive to the assumed form of climatic248

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influences on SARS-CoV-2 transmission, which we have taken here to be very similar to those249

of the related �–CoV HCoV-HKU1. Indeed, even with the incorporation of NPIs (which in250

general may be adopted differently than the scenarios considered here), the clinical burden of251

subsequent infection peaks is sensitive to the relative fraction of primary and secondary cases as252

well as the fraction of severe cases for each category, which intimately depend on the nature of253

the adaptive immune response. In turn, the severity of an infection could affect the nature of the254

subsequent adaptive immune response through antigen priming or T cell exhaustion. Finally,255

the disease dynamics predicted by the model can be substantially altered using a highly simpli-256

fied scenario for the introduction of a vaccine, although the achievable reductions in infections257

are strongly dependent on the efficacy of the vaccine and the nature of the adaptive immune258

response. Nevertheless, even with imperfect vaccine immunity, reductions in the number of259

primary cases through vaccination may have important clinical implications.260

261

Altogether, this work emphasizes the complex dependence of the immune landscape gener-262

ated by SARS-CoV-2 infection on the presently largely unknown nature of the adaptive immune263

response to this virus and the efficacy of potential future vaccines. Depending on how these un-264

fold, the model predictions for future clinical burdens range from sustained epidemics to near265

case elimination. Consequently, accurately characterizing the nature of immunity to SARS-266

CoV-2 will be critical for the management and control of future infections.267

Acknowledgements268

CMSR acknowledges support from the Natural Sciences and Engineering Research Council of269

Canada through a Postgraduate-Doctoral Scholarship. CEW is an Open Philanthropy Project270

fellow of the Life Sciences Research Foundation. REB is supported by the Cooperative Insti-271

tute for Modelling the Earth System (CIMES). SAL and CMSR acknowledge support from the272

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James S. McDonnell Foundation 21st Century Science Initiative Collaborative Award in Under-273

standing Dynamic and Multi-scale Systems. SAL acknowledges support from the C3.ai Digital274

Transformation Institute, the National Science Foundation under grant CNS-2027908, and the275

National Science Foundation Expeditions Grant CCF1917819. BTG acknowledges support276

from the US CDC.277

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16



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27. A. D. Becker, B. Grenfell, PLoS ONE 12, e0185528 (2017).312

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eng.htm.323

36. Assuming a simplified scenario in which a constant proportion of the total population is324

vaccinated weekly, the proportion of the population that is not vaccinated U can be modeled325

to decrease exponentially in time as U(t) = exp(�⌫t). Consequently, in order to achieve326

27% vaccination coverage after an 8 month (or 34.7 week) period (i.e. U(34.7) = 0.73),327

a weekly vaccination rate of 0.91% of the remaining unvaccinated population would be328

required.329

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17



https://doi.org/10.1101/2020.07.15.20154401


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0.02

0.04

0.06

0.0

0.1

0.2

0.3

0.4

0.00

0.02

0.04

0.06

Years

�SP

��SS

IP

IS� = 0.5 � = 1

� = 0.5 � = 1

0 1 2 3 4 5 0 1 2 3 4 5

0 1 2 3 4 5 0 1 2 3 4 50.0

0.1

0.2

0.3

0.4

0.00

0.02

0.04

0.06

0.0

0.1

0.2

0.3

0.4

0.00

0.02

0.04

0.06

Years

�SP

��SS

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IS

Partial

Primary

Secondary

("#!)

(%"#")

(&!)

(&")

NPINo NPI

3 Figure 3

0.000

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0.00 0.25 0.50 0.75 1.00Susceptibility to secondary infection (�)

Vacc

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rate

(�) Duration

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1

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pop

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Frac

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Time (years)

Time (years)



Fully susceptibleImmunePartially immune

ν0.001

0.0050.009

ν0.0010.005

0.009

ν0.005

0.009

Fully susceptibleImmunePartially immune

0.001

Frac

tion

of p

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atio

n

Time (years) ν0.0010.005

0.009

e

d

c

fb

0.50.71

ν

!! "#$%(years)

Susceptibility to secondary infection "

Herd immunity

Frac

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infe

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at e

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briu

m

a

3

4 Figure 4

c d

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Natural immunity

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Primary infection

Secondary infection

0.0000

0.0025

0.0050

0.0075

Seve

re c

ases

0.00

0.25

0.50

0.75

1.00

1 2 3 4 5Time (years)

Frac

tion

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n

0.0000

0.0025

0.0050

0.0075

Seve

re c

ases

0.00

0.25

0.50

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0.0000

0.0025

0.0050

0.0075

Seve

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0.00

0.25

0.50

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Frac

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0.0000

0.0025

0.0050

0.0075

Seve

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0.00

0.25

0.50

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Frac

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0.0000

0.0025

0.0050

0.0075

Seve

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0.00

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0.0000

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0.0000

0.0025

0.0050

0.0075

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0.00

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Frac

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0.0000

0.0025

0.0050

0.0075

Seve

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0.00

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Frac

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0.0000

0.0025

0.0050

0.0075

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0.00

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Frac

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0.0000

0.0025

0.0050

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Frac

tion

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0.0000

0.0025

0.0050

0.0075

Seve

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0.00

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Frac

tion

of p

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n

0.0000

0.0025

0.0050

0.0075

Seve

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0.00

0.25

0.50

0.75

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Frac

tion

of p

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0.0000

0.0025

0.0050

0.0075

Seve

re c

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0.00

0.25

0.50

0.75

1.00


Frac

tion

of p

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atio

n

0.0000

0.0025

0.0050

0.0075

Seve

re c

ases

0.00

0.25

0.50

0.75

1.00


Frac

tion

of p

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atio

n

0.0000

0.0025

0.0050

0.0075

Seve

re c

ases

0.00

0.25

0.50

0.75

1.00


Frac

tion

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n

0.0000

0.0025

0.0050

0.0075

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ases

0.00

0.25

0.50

0.75

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Frac

tion

of p

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n

Short-lasting, partially protective natural immunity, enhanced disease severity upon secondary infection, no vaccination

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4

immuno-epidemiological life-history and the dynamics of ...€¦ · 15/07/2020 ·...

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