key: cord-0984425-la63vi50
authors: Bewick, S.
title: Viral Variants and Vaccinations: If We Can Change the COVID-19 Vaccine, Should We?
date: 2021-01-06
journal: nan
DOI: 10.1101/2021.01.05.21249255
sha: 7ad809cb899dce8e7d6f75c8a94bb3ae9db94128
doc_id: 984425
cord_uid: la63vi50

As we close in on one year since the COVID-19 pandemic began, hope has been placed on bringing the virus under control through mass administration of recently developed vaccines. Unfortunately, newly emerged, fast-spreading strains of COVID-19 threaten to undermine progress by interfering with vaccine efficacy. While a long-term solution to this challenge would be to develop vaccines that simultaneously target multiple different COVID-19 variants, this approach faces both developmental and regulatory hurdles. A simpler option would be to switch the target of the current vaccine to better match the newest viral variant. I use a stochastic simulation to determine when it is better to target a newly emerged viral variant and when it is better to target the dominant but potentially less transmissible strain. My simulation results suggest that it is almost always better to target the faster spreading strain, even when the initial prevalence of this variant is much lower. In scenarios where targeting the slower spreading variant is best, all vaccination strategies perform relatively well, meaning that the choice of vaccination strategy has a small effect on public health outcomes. In scenarios where targeting the faster spreading variant is best, use of vaccines against the faster spreading viral variant can save many lives. My results provide rule of thumb guidance for those making critical decisions about vaccine formulation over the coming months.

180 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint where % 5 &" !,#,6,'(∆' = ' + 1, " !,#,$,'(∆' = + − 1 ." !,#,6,' = ', " !,#,$,' = +/ is the probability of 181 an individual with vaccination status M receiving the vaccine and transitioning to vaccination 182 status U, T 6 is the rate at which the vaccine is administered and X is the fraction of the 183 population willing to receive a vaccine. 100% of the population is willing to/forced to receive the vaccine, and that 5000 people per day, 198 can be vaccinated in a 500,000 person population (i.e., it takes 100 days or approximately 3 199 months to vaccinate the entire focal population).

For initial conditions, I assume that, at the start of the simulation, a pre-defined fraction 201 of the population, Y 0 , is infected with the first viral variant, and a pre-defined fraction of the 202 population, Y 1 , is infected with the second viral variant. I ignore co-infections at the beginning of 203 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 6, 2021. ;

the simulation under the assumption that Y 0 Y 1 ∑ " .,+,$ -.,+,$ -≪ 1 for reasonably small Y 0 and/or Y 1 .

Likewise, I assume that, at the start of the simulation, a pre-defined fraction of the population, 205 [ 0 , is immune as a result of previous infection with the first viral variant, and that a pre-defined 206 fraction of the population, [ 1 , is immune as a result of previous infection with the second viral 207 variant. As with infection, I assume that there are no individuals who have acquired natural 208 immunity to both viruses, which is a good approximation when either [ 0 or [ 1 are small (at least 209 one strain has not been circulating for a long time) or when 9 01 or 9 10 are large (natural cross-210 protection is high, making serial infection with different strains less likely). In practice, most 211 simulations that I consider assume that the second COVID-19 strain is a recent introduction, and is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

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In the analysis that follows, I consider three different vaccination strategies. First, I consider a CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint social distancing may be required, particularly for at-risk people. For all simulations, I assume 240 that the first viral variant spreads at a slower rate (i.e., is less transmissible) than the second. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint with one of the two virus strains, then approximately 3000 individuals will die. Likewise, if the entire population is infected with both of virus strains (simultaneously or sequentially), then 259 approximately 6000 individuals will die. Because herd immunity is typically achieved at 260 infection rates less than 100%, 3000 and 6000 deaths represent upper bounds for single 261 infections and double infections respectively. Nevertheless, these bounds help to frame 262 simulation results.

As expected, when cross-protection is close to zero, vaccination against one of the two 264 viral strains cuts the total death rate in half. However, it does nothing to prevent deaths from the 265 off-target viral variant. Because of this, vaccination against the more transmissible virus (in this 266 case, viral variant 2) is almost always optimal, even if the less transmissible virus is initially 267 present at substantially higher rates. This is because, regardless of initial conditions, the off-268 target variant will inevitably sweep the population. The virus that is more transmissible, 269 however, will infect a higher proportion of the population prior to reaching herd immunity.

Consequently, vaccinating against this more transmissible strain is the better option when there is 271 little to no cross-protection.

Although faster spread of viral variant 2 is the primary factor favoring use of this strain as 273 the vaccine target at low levels of cross-protection, there are two additional advantages to 274 focusing on viral variant 2. Both are related to the fact that viral variant 1 is more prevalent.

While somewhat counterintuitive, higher prevalence of a particular strain prior to vaccination 276 can actually make it less effective to target that strain with the vaccine (see Fig. 5 ). This is 277 because higher viral prevalence goes hand-in-hand with higher levels of natural immunity, which 278 has two consequences. First, if one of the two viral variants will inevitably sweep the population 279 (i.e., low cross-protection), then it is preferable that this be the variant with more existing natural 280 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint immunity, since fewer additional deaths will be necessary to reach herd immunity. Second, when the vaccine is targeted against the more prevalent variant, more vaccine doses are wasted 282 protecting individuals who are already naturally immune (see Figure 5 ). By contrast, wasted 283 vaccine doses less common when the vaccine protects against a strain without much pre-existing 284 natural immunity. Again, this disfavors use of the more prevalent strain as the vaccine target (in 285 this case, variant 1).

Interestingly, a relatively high level of cross-protection is required before vaccination 287 with the more prevalent but slower spreading variant becomes a competitive strategy. Increasing 288 cross-protection from 0% to 50%, for instance, only reduces total deaths by <30% when the 289 vaccine is targeted against the prevalent but slow spreading variant 1. By contrast, cross-290 protection has a much stronger effect earlier on when the vaccine is targeted against the fast 291 spreading variant 2. In this case increasing cross-protection from 0% to 50% causes a >70% 292 reduction in deaths. Notably, even at 90% cross-protection, vaccination against the slow 293 spreading variant still underperforms in terms of preventing deaths. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint Like deaths, peak infections are also much higher under the scenario with vaccination against the prevalent but slow spreading variant 1. Interestingly, however, peak infections are 305 also higher for the mixed vaccination strategy as compared to vaccination against viral variant 2, 306 at least when cross-protection <50%. This contrasts what was seen for total deaths. Nevertheless, 307 the mixed strategy still performs substantially better than vaccination against the slow spreading 308 variant 1 over most of the range of potential cross-protection levels. At high cross-protection, 309 (80-90%), differences in the different vaccination strategies are minimal, and the mixed strategy, 310 or even vaccination against the slow spreading viral variant can actually yield lower peak 311 infection levels.

Times to viral extinction tend to be unimodal, at least for strategies that target a single 313 viral variant. This is because, at low cross-protection, the off-target variant rapidly sweeps the is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint emerge despite the relatively high cross-protection levels (9 01 = 9 10 = 0.7) assumed in Figure 2 Figure 3 , I assume a population size of 500,000 individuals, thus it would take 100 385 days to vaccinate the entire population at a rate of 5000 people/day, and 50 days to vaccinate the 386 entire population at a rate of 10000 people/day. As expected, total deaths and peak infection rates 387 decrease sharply with increased rate of vaccination roll-out for all vaccination strategies.

. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; vaccination strategies in terms of total deaths, and outperforms vaccination against variant 2 in 406 terms of peak infections when the entire population can be vaccinated within 100 days. Further, 407 when full vaccination can be completed within ~60 days (2 months), vaccination against the first 408 viral variant actually leads to the lowest peak infection rates, though it still gives higher total 409 deaths than the mixed vaccination strategy. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint Table 1 . 475 Results shown are median values over 30 trials. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. is 100-to 1000-fold more prevalent at the onset of the vaccination period and even when cross-525 protection is relatively high. This outcome is a direct result of the nature of exponential growth.

In particular, exponential growth rapidly accentuates even slight differences in populations with 527 different exponential growth rates (or different R0 values, in the case of diseases). As a 528 consequence, over a matter of days to months, any initial advantage of the more prevalent but 529 slower spreading viral variant is rapidly swamped by the diverging trajectories of the viral 530 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint growth curves. Surprisingly, while targeting the slow spreading variant is rarely beneficial, a mixed strategy, where 50% of the population receives a vaccine against one strain, and 50% 532 receives a vaccine against the other strain, can perform relatively well, at least when the 533 differences in viral transmission rates are not extreme (e.g. the second viral variant is £50% more 534 transmissible than the first). That said, for more extreme differences in transmission rates, the 535 mixed strategy rapidly loses traction, and vaccination against the fast-spreading viral variant can 536 save numerous lives, as well as lower peak infection rates, even relative to the mixed strategy.

While most realistic scenarios that I consider suggest that it is best to develop vaccines 538 against the faster-spreading viral variant, this is not universally true. Factors that promote the 539 viability of vaccination against the slow-spreading variant include smaller differences in growth 540 rates between the two viral strains (see Figure 2 ), as well as faster vaccine roll-outs that leave 541 less time for the fast-spreading virus to overcome its initial lower prevalence (see Figure 3) . In CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted January 6, 2021. immunity. This simplifying assumption is most appropriate if the first dose of vaccine either 560 does not provide much immunity, or else provides nearly complete protection. Predictions will 561 be less accurate, however, if the first dose provides partial immunity that is then increased by the 562 second dose. Another simplifying assumption of my model is that the population is well-mixed 563 and without any structure like age-classes or differences in behavior (e.g., ability to 564 telecommute, willingness to wear masks) that might lead to differential interactions among 565 groups or else different exposure rates or susceptibilities to exposures. As well, I do not consider 566 an exposed class or waning immunity. Likewise, I do not consider differences in infectious 567 period or disease outcomes that may be garnered by immunity, either to the infecting strain or to 568 the off-target strain. In reality, though, it is likely that vaccination would, at the very least, lower 569 death rates of an infection, even if it does not fully protect against infection itself. Another 570 assumption that I make is that, other than transmission rates, both viral variants are largely 571 identical. That is, they induce similar death rates, have similar recovery rates, and illicit similar CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 6, 2021. ; https://doi.org/10.1101/2021.01.05.21249255 doi: medRxiv preprint information becomes available about newly emerging strains, their relative transmissibilities and 576 the degree of cross-protection, including additional model details and complexities will become 577 more feasible. 578 Overall, my model suggests that, except in very rare instances, monovalent COVID-19 579 vaccines should target the fastest-spreading strain of the virus, regardless of how prevalent that 580 strain is at the outset of the vaccination period, and regardless of the degree of cross-protection 581 offered by either vaccines or natural immunity. For scenarios where targeting the slower-582 spreading strain is equivalent or even marginally better than targeting the faster-spreading strain, 583 total deaths and peak infection rates tend to be low for all vaccination strategies. However, for 584 scenarios where targeting the faster-spreading strain is best, differences in total deaths and peak 585 infections can be substantial. Thus, even from a precautionary principle, the safest bet is to target 586 the variant with the higher transmission rate. The mixed strategy -vaccinating half of the 587 population against each viral variant -performs nearly as well as vaccinating against the fast 588 spreading virus over a surprisingly large range of viral transmission rates. However, when the 589 fast spreading virus is significantly more transmissible than the original strain, even the mixed 590 strategy can result in a sizeable number of additional deaths as compared to vaccination solely 591 against the fast spreading strain. Thus, for example, for the low estimate that the B.1.1.7 strain is 592 50% more transmissible than its predecessor, the mixed vaccination strategy is nearly as good as 593 vaccination against B.1.1.7 alone. However, for the high estimate that the B.1.1.7 strain is 70% 594 more transmissible, the mixed strategy dramatically underperforms, leading to nearly 70% more 595 deaths as compared to a strategy where all vaccine efforts are focused on the B.1.1.7 strain.

New strains of COVID-19 will continue to emerge that are more transmissible than the 597 current variants, and that escape or partially escape from the current vaccines. Although we 598 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted January 6, 2021. ; cannot prevent this from happening, we can make decisions about vaccination strategies that minimize the negative health outcomes of such events. Naturally, the best long-term solution will 600 be to develop multivalent mRNA vaccines that simultaneously protect against all dominant 601 COVID-19 viral variants in circulation. Until that is possible, however, my study provides 'rule-602 of-thumb' guidance for public health officials and vaccine companies alike. Specifically, my 603 study suggests that, in most cases, targeting vaccines against the fastest spreading viral variant 604 will at worst perform equally well as other strategies and, at best, save many lives.

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