key: cord-0939560-ioclf03d authors: Gerrish, P.; Saldana, F.; Galeota-Sprung, B.; Colato, A.; Rodriguez, E.; Velasco-Hernandez, J. X. title: How unequal vaccine distribution promotes the evolution of vaccine escape date: 2021-03-28 journal: nan DOI: 10.1101/2021.03.27.21254453 sha: ed98ef0f1a88ac5050ee2c128ac085c326832886 doc_id: 939560 cord_uid: ioclf03d In the context of the ongoing SARS-CoV-2 pandemic, health officials warn that vaccines must be uniformly distributed within and among countries if we are to quell the pandemic. Yet there has been little critical assessment of the underlying reasons for this warning. Here, we explicitly show why vaccine equity is necessary. We begin by drawing an analogy to studies showing how disparities in drug concentration within a single host can promote the evolution of drug resistance, and we then proceed to mathematical modeling and simulation of vaccine escape evolution in structured host populations. Perhaps counter-intuitively, we find that vaccine escape mutants are less likely to come from vaccinated regions where there is strong selection pressure for vaccine escape and more likely to come from a neighboring unvaccinated region where there is no selection for escape. Unvaccinated geographic regions thus provide evolutionary reservoirs from which vaccine escape mutants can arise and infect neighboring vaccinated regions, causing new local epidemics within those regions and beyond. Our findings have timely implications for vaccine rollout strategies and public health policy. vaccines are two stellar examples of highly effective vaccines to which the respective viruses have not evolved escape strains. Flu vaccines, on the other hand, are notoriously "leaky", with rampant vaccine escape emerging every flu season and creating the need for a new flu vaccine every year. Vaccine escape has effectively prevented the development of an HIV vaccine because mutants able to "escape" any conceivable vaccine target preexist in circulating virus. Where the many different SARS-CoV-2 vaccines stand in this wide spectrum of vaccine-escape susceptibility is still a matter of debate, but increasingly the evidence indicates escape is a real threat [6, 12, 14, 16, 22, [31] [32] [33] . The E484K mutation in the backgrounds of UK variant B.1.1.7 or South African variant B.1.135 are two particularly worrisome variants [14, 32] . There is even some concern, and evidence, that new variants may be able to evade natural immunity to SARS-CoV-2 in previously-infected hosts through "immune escape" [9, 14, 31] ; this does not bode well for prospects of lasting vaccine-induced immunity [1, 20] . Finally, a recent study [8] reveals that closely-related endemic human coronavirus 229E displays evidence of "antigenic drift" -the same process of rapid antigenic evolution that occurs in Influenza. Vaccine escape can be viewed as analogous to drug resistance. In the evolution of drug resistance, it is wellestablished that "privileged sites" in an infected host in which the administered drug is somehow restricted due to physiological constraints (e.g, the blood-brain barrier [19] ), can play a very key role [3, 17, 19] . In such sites, the population size of the infectious agent can remain large because there is essentially no drug to suppress it. In these large sub-populations, mutants that are resistant to the drug can increase in frequency without selective constraints for or against. When resistant mutants from such privileged sites migrate back into sites with unrestricted drug concentrations, these "unprivileged sites" quickly succumb to fixation of resistant mutants. The same phenomenon is well-documented in biofilms [7, 17, 28, 30] , wherein regions of a biofilm that are shielded from antibiotics provide reservoirs in which resistance mutations evolve neutrally and can subsequently migrate to unshielded regions, rendering the antibiotic ineffective in these regions and eventually in the entire biofilm. The same principle even applies to cancer: disparities in drug concentration can promote the evolution of drug resistance [11] . The lessons learned from drug resistance point to two key factors that could facilitate the evolution of vaccine escape, namely, population size and population structure [5, 18] . Population size is important because the overwhelming majority of mutations occur during replication. Smaller populations mean fewer replications which means reduced opportunity for mutations to arise; this simple principle is the basis for health officials' repeated pleas for continued social distancing and facemask usage (in the context of the current SARS-CoV-2 pandemic) despite the existence of vaccines. Population structure is important because local epidemics can 3 . CC-BY-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 March 28, 2021. ; https://doi.org/10.1101/2021.03.27.21254453 doi: medRxiv preprint vary in size and vaccine coverage and thus harbor the vaccine equivalent of privileged sites, mentioned above, albeit at the host-population and not within-host level. A recent study [13] looks at the effects of different kinds of population compartmentalization on the risk of vaccine escape, namely, age and vulnerability. A further lesson from drug resistance studies derives from the observation that variability in drug distribution can have more of an impact on the evolution of resistance than overall drug concentration [5, 18] . Extrapolating to vaccine escape, this would indicate that geographic variability in vaccine distribution can pose a bigger threat of vaccine escape than factors such as public distrust and fake news that reduce vaccine participation throughout the population. To assess claims that vaccine equity is essential, and to validate our verbal extrapolations from drug resistance evolution, we employ mathematical models and simulations of vaccine escape evolution. In our basic model, there are just two local epidemics in geographically neighboring regions or "patches". One patch has access to a vaccine, the other does not. We study how the unvaccinated patch affects the probability of vaccine escape in the vaccinated patch. We can assume that an escape mutant will always have a selective advantage in a vaccinated population (SM), simply because there is a larger number hosts it can infect (susceptible and vaccinated hosts) than the wildtype (infects susceptible hosts only). Thus, we do not need to explicitly model the transmission of and dynamics of escape mutants after they have emerged; we can focus simply on the timing of emergence of the first escape mutant. To this end, we simply model the accumulation of escape mutations from wildtype and focus on the timing of the first infection event in which a new host is infected with an escape mutant, which we will call an "escape-infection" event. In vaccinated Patch 1, there will be strong selection for vaccine escape but limited opportunity for escape mutations to arise simply because of the reduced number of unvaccinated susceptible hosts. In unvaccinated Patch 2, escape mutations have no selective advantage, but there is a larger number of unvaccinated susceptible hosts. Our model is described by the following equations: where S j , V j , I j , E j , and R j are the fraction of the population that are susceptible, vaccinated, infected, 4 . CC-BY-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 March 28, 2021. ; https://doi.org/10.1101/2021.03.27.21254453 doi: medRxiv preprint infected with escape mutant, and recovered, respectively, in Patch j; β ij is the transmission rate from Patch i to Patch j (β jj is the transmission rate within Patch j); φ j is vaccination rate in Patch j; γ is recovery rate; U is a composite per-host mutation rate from wildtype virus to escape mutant virus (see discussion below); n is number of patches; dots indicate time derivatives. We note the absence of a contagion term in the equation for E j . This term is not needed for our purposes because our focus is only on the first escape-infection event -a discrete event. Furthermore, this term can lead to erroneous results because ours is a continuous model: a contagion term would allow for transmission to fractions of individual hosts that can erroneously amplify the vaccine escape mutant prior to the first escape-infection event. Here, we assume there are only two patches, n = 2 and j ∈ [1, 2] . Our more complex models and detailed simulations are described in the Supplementary Materials (SM). We define random variable T ij as the time of the first infection event in which a new host in Patch j is infected by an escape mutant that arose in Patch i. Such infection events occur with rate r ij (t) = β ij E i (t)(S j (t) + σV j (t)), where σ allows for varying levels of escape reflecting the observed spectrum of partial immunity against different variants ranging from no escape σ = 0 to full escape σ = 1. For now, we will assume intra-patch transmission rates are equal, β jj = β, and inter-patch transmission rates are equal, β ij | i =j = β × . We let β × = λβ and we assume λ 1 to reflect the fact that inter-patch transmission will typically be much less frequent than intra-patch transmission. We define random variable T f as the time at which the last infected individual recovers. The three quantities of interest are: 1) p = P{T 11 > T 21 | T 12 < T f ∨T 11 < T f }, the probability that vaccine escape in Patch 1 comes not from Patch 1 but from neighboring unvaccinated Patch 2, conditioned on vaccine escape emerging in Patch 1 from one of the two patches, 2) f = P{T 21 < T f ∨ T 11 < T f }/P{T 11 < T f }, the factor by which the probability of vaccine escape in Patch 1 is increased by having neighboring unvaccinated 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 March 28, 2021. ; https://doi.org/10.1101/2021.03.27.21254453 doi: medRxiv preprint corner of parameter space -in the context of the ongoing SARS-CoV-2 pandemic -is Israel and its neighbors: Israel presently has the highest vaccine coverage in the world [24] while its neighbors have among the lowest. Our findings would recommend vigilance for vaccine escape in this and many other areas of the world that have significant disparity in vaccine distribution both between and within countries. Figure 2 explicitly shows the effect of vaccine disparity between the two patches. Equal vaccination between the two patches gives the lowest probability of vaccine escape. Curiously, for medium to high reproductive numbers and low mutation rates, moderate disparities in vaccination can promote the emergence of vaccine escape more strongly than extreme (all or nothing) disparities. Our parameter U is a composite parameter: it is the rate at which the transmission chain among hosts finally leads to one host infecting another host with a vaccine escape mutant, which we refer to above as an escape-infection event. As such, this parameter incorporates the mutation rate of the virus as well as any effect on within-host fitness it may have: a decrease (increase) in within-host fitness will effectively decrease (increase) U . Within-host fitness of SARS-CoV-2 should not be affected by humoral immunity of the host because transmissibility of SARS-CoV-2 peaks around the time of onset of symptoms [15] , whereas a robust antibody response is not mounted until roughly ten days after the onset of symptoms [15, 29] . Thus any effect that escape mutations have on within-host fitness will not be antigenic in nature and will thus expose any pleiotropic fitness effects of vaccine escape. In this light, U may be viewed as primarily encapsulating two factors: viral mutation rate, and any pleiotropic fitness effect vaccine escape may have. The parameters of our model most readily affected by public policy are λ, β and φ j : λ can be reduced, for example by closing borders or otherwise limiting the movement of people, β can be reduced by facemasks and social distancing, and φ j can be made more uniform by equitable vaccine distribution. As vaccines become increasingly available, restrictions on movement and contact are slowly being lifted in parallel, increasing both λ and β. The relaxation of these restrictions may have adverse effects if done too quickly [2, 26, 27] , and may further increase the probability of vaccine escape. Our findings provide a solid theoretical basis to support arguments for vaccine equity. Geographic regions of the human population that are not being vaccinated can serve as evolutionary reservoirs from which vaccine escape mutations may arise and give rise to renewed and unfettered spread of SARS-CoV-2. It may be that vaccine escape is inevitable and that SARS-CoV-2 will eventually become endemic [4, 23] , in which case vaccine updating and exploration of new antigenic targets [10] will become the norm. Or we may have a window of opportunity now to prevent that outcome, in which case present vaccine rollout strategies could 6 . CC-BY-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 March 28, 2021. ; https://doi.org/10.1101/2021.03.27.21254453 doi: medRxiv preprint make the difference. Vaccine updating, optimizing deployment of the many different available vaccines [21] and, as we have shown, vaccine equity, are key ingredients of these strategies. . CC-BY-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 March 28, 2021. ; https://doi.org/10.1101/2021.03.27.21254453 doi: medRxiv preprint . CC-BY-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 March 28, 2021. ; Vaccination rate , φ 1 Vaccination rate, φ 1 Fig 1 Representative plots of: p, the probability that vaccine escape emerging in vaccinated Patch 1 comes not from Patch 1 but from Patch 2 (left column), and f , the factor by which the probability of vaccine escape emerging in Patch 1 is increased as a consequence of having unvaccinated neighboring Patch 2 (right column). Horizontal axes indicate Patch 1 vaccination rate, φ 1 , and φ 2 = 0. Parameters not specified in the plots are: λ = 0.02, γ = 0.1, β = γR 0 , and N = 10 5 . Expressions for p and f are specified in the main text and derived in the SM. For these plots, we have assumed that vaccination begins at the time the epidemic begins. Departures from this assumption as well as exploration of parameter space are in the SM. . CC-BY-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. Vaccine escape factor, ε, is plotted as a function the fraction of vaccine that goes to Patch 2. Vaccine escape factor is defined as vaccine escape probability divided by the escape probability when all vaccine goes to one of the two patches (maximum disparity). Parameters are: λ = 0.05, γ = 0.1, β = γR 0 , N = 10 5 and left column: V (0) = 0, φ 1 + φ 2 = 0.05; middle column: V (0) = 0.2, φ 1 + φ 2 = 0.02; right column: V (0) = 0.6, φ 1 + φ 2 = 0.1. . CC-BY-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. 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P.G. and A.C. received financial support from the USA/Brazil Fulbright scholar program. J.V. and F.S. received financial suppot from grants DGAPA-PAPIIT UNAM IV100220 and DGAPA-PAPIIT IN115720 UNAM.