The spillover of zoonotic pathogens from wild animal reservoirs into the human population is becoming an ever more frequent, but still largely unpredictable occurrence with significant negative impacts on human health (Plowright et al., 2017). Even the most predictable zoonoses, such as Lassa fever virus from Mastomys natalensis and rabies from feral dogs, are estimated to kill thousands of individuals per year worldwide (Richmond & Baglole, 2003; Taylor & Nel, 2015). Less predictable spillover events also create large public health impacts. For instance, the 2014 West African Ebola epidemic killed more than 11,000 people over the course of the 30‐month epidemic (Kaner & Schaack, 2016), and outbreaks of SARS and MERS have killed hundreds (de Wit, Doremalen, Falzarano, & Munster, 2016). Although large‐scale vaccination campaigns of wild animals have shown the ability to reduce spillover events in temperate regions (e.g., Europe and North America for rabies in red foxes and raccoons), similar efforts cannot provide the coverage needed for control of most emerging zoonoses because of difficulties in reaching wildlife populations with conventional vaccines in the more remote and inaccessible environments where these pathogens frequently emerge.
One promising innovation for the vaccination of wildlife is the use of transmissible, rather than individually administered, vaccines. Conventional, nontransmissible vaccines protect only those individuals directly vaccinated (e.g., administered parenterally or through bait). In contrast, transmissible vaccines have the potential to reach more of the targeted wildlife population through animal‐to‐animal transmission. A transmissible vaccine works on the same principles as other live vaccines—following administration to an individual, the vaccine leads to stimulation of a protective immune response—but with its capacity for transmission, the vaccine is able to spread and immunologically protect other susceptible individuals beyond those directly vaccinated. Results from mathematical modeling indicate that transmissible vaccines substantially increase vaccine coverage and thereby the scope for pathogen elimination or eradication (Basinski et al., 2018; Nuismer et al., 2016; Nuismer, May, Basinski, & Remien, 2018). To date, transmissible vaccines remain largely untested. However, a transmissible vaccine comprised of an attenuated myxoma virus encoding an antigen from rabbit hemorrhagic fever virus (RHFV) was able to transmit between rabbits and proved protective against both myxoma and rabbit hemorrhagic fever (Angulo & Barcena, 2007; Bárcena et al., 2000). Efforts are now underway to develop transmissible vaccines targeting other pathogens in wildlife populations including Ebola and Lassa fever viruses in their natural animal reservoirs (Marzi et al., 2016; Murphy, Redwood, & Jarvis, 2016; Tsuda et al., 2011, 2015).
Of the two most common types of live vaccines, attenuated and recombinant vectored, the latter appears to be the most promising for development as a transmissible vaccine platform (Bull, Smithson, & Nuismer, 2018; Murphy et al., 2016). Recombinant vector vaccines (RVVs) consist of an antigen‐expressing pathogen gene(s) engineered into a competent but avirulent viral vector (Bull et al., 2018). The possible combinations afforded by this approach appear almost unlimited, and the ability to choose vectors from a wide range of possibilities should permit rates and pathways of vaccine transmission to be tuned to at least some degree. However, recombinant vaccines face regulatory issues due to their genetically modified status, and the ability to transmit—a big advantage in pathogen control—may provide a hurdle to regulatory approval. There are multiple means by which transmissible RVVs may overcome potential regulatory issues for their use in wildlife populations. If the vaccine is only weakly transmissible (e.g., R0<1), the vaccine will inevitably approach extinction once it is no longer being directly administered to the target population (Nuismer et al., 2016). Similarly, if the vector occurs naturally in the host population, vector‐specific immunity may lead to vaccine extinction (Basinski et al., 2018). Finally, if the RVV is genetically unstable and progressively evolves to delete or downregulate the inserted transgene, the vaccine may revert over time, leaving behind only the original viral vector.
Although previous work has studied the efficacy of weakly transmissible vaccines and explored how cross‐immunity between vector and vaccine can influence vaccine performance (Basinski et al., 2018; Nuismer et al., 2016), the consequences of genetic instability for transmissible vaccines have not yet been rigorously evaluated. As a result, it is currently unclear what level of instability can be tolerated for a transmissible vaccine to remain effective, or how unstable a transmissible vaccine needs to be to guarantee its ultimate extinction. This balance between immunogenicity and target antigen loss will dictate whether vaccine decay is slow enough to enable broad protection against a target pathogen but fast enough to ensure vaccine extinction in a reasonable time frame.
In the present study, we develop and analyze mathematical models and computer simulations of transmissible recombinant vector vaccines. Our models explicitly integrate genetic instability by allowing the vaccine to revert to viral vector. We consider scenarios where cross‐immunity between vector and vaccine is absent as well as scenarios where cross‐immunity is strong. We use these models to identify the amount of genetic instability that can be tolerated for a transmissible vaccine to remain effective, and to evaluate the scope for tuning genetic instability for maximal efficacy while ensuring vaccine extinction.
An absence of cross‐immunity might accrue to a RVV if prior vaccine exposure and the resultant host adaptive immune response does not biologically impact vaccine re‐infection as reported for cytomegalovirus—(Gandhi & Khanna, 2004) or if immunity to the foreign antigen is highly immunodominant, minimizing other immunological responses to the vector. In the absence of cross‐immunity, the dynamics of the transmissible vaccine and pathogen can be described without explicitly tracking the density of vector generated by reversion: When a reversion transforms vaccine to vector, the host that was vaccine‐infected merely moves back into the pool of susceptible hosts. Consequently, we need follow only the densities of hosts susceptible to vaccine and pathogen (S), infected with vaccine (V), infected with pathogen (P), or recovered from vaccine infection (RV) or pathogen infection (RP) and immune to infection by both vaccine and pathogen. The following system of differential equations applies:(1a)dSdt=b1-σ-βVSV-βPSP-dS+uV
(1e)dRPdt=γPP-dRPwhere all parameters and variables are defined in Table 1. For simplicity, we assume immunity to the pathogen and vaccine is perfect and lifelong.
Although some viral vectors are expected to elicit little if any cross‐immunity (i.e., CMV), in other cases at least some degree of cross‐immunity is likely. To bracket the range of possible scenarios, our second model assumes the opposite extreme of the first: complete cross‐immunity between vector and vaccine. Integrating cross‐immunity necessitates a more complex model where the dynamics of the vector are tracked explicitly. In this model, when a reversion transforms the vaccine into vector, the revertants are removed from the vaccine‐infected class (V) and moved to the vector‐infected class (M). Because the vector no longer carries or expresses pathogen genes, vector and pathogen share no cross‐immunity and can co‐infect. In contrast, because we assume the vaccine carries both pathogen and vector genes that elicit an immune response, cross‐immunity exists between vaccine and pathogen and vaccine and vector. We assume this cross‐immunity is complete and precludes co‐infection (Basinski et al., 2018). These assumptions give rise to the following system of differential equations:(2a)dSdt=b1-σ-βVSV+M~-βPSP~-dS
(2k)dRPMdt=γPPM+γVMP-dRPMwhere P~=PS+PM+C and M~=MP+MS+C are the total number of animals infected with pathogen and revertant vaccine, respectively, and all other parameters and variables are as defined in Table 2. Transmission rates and recovery rates of vector and vaccine are identical, and immunity is perfect and lifelong (as before).
In the absence of cross‐immunity between vaccine and viral vector, identifying conditions where a transmissible vaccine precludes pathogen invasion is straightforward (Appendix 1). A population can be protected from pathogen invasion if the transmissible vaccine is administered to newborn individuals at a rate that exceeds the following threshold:(3)σcrit=1-1R0,P1-R0,VR0,P+μd+γV
where R0,V is the basic reproductive number of the vaccine. This result generalizes our previous work for a transmissible vaccine that does not decay (Nuismer et al., 2016).
This threshold can be used to define the conditions under which a transmissible vaccine will outperform a standard vaccine. Specifically, dividing the right‐hand side of (3) by the vaccination rate required to achieve prophylaxis using a conventional vaccine 1-1R0,P, yields the following expression for the relative performance of a transmissible vaccine that experiences reversion to viral vector:(4)ρ=1-R0,VR0,P+μd+γV
If ρ is less than one, a transmissible vaccine will outperform a conventional, directly administered vaccine. If, in contrast, ρ is greater than one, a transmissible vaccine will perform worse than a traditional vaccine. This result seems to defy intuition—that transmission could be worse than no transmission. However, it stems simply from the assumption that individuals infected with the transmissible vaccine are allowed to decay into susceptibles (at rate μ) without first gaining immunity to the target pathogen. Thus, individuals that are directly vaccinated can “lose” the vaccination, something not allowed in the model lacking vaccine transmission. Were the comparison restricted to the same rates of decay for a nontransmissible vaccine as for a transmissible vaccine, transmission would always provide greater coverage.
Inspection of (4) demonstrates that the relative performance of a transmissible vaccine depends on its rate of reversion to insert‐free vector (Figure 2). Specifically, if the reversion rate is small relative to host death rate, d, and recovery rate from vaccine/vector infection, γV, reversion has only a very slight impact on vaccine performance (Figure 2). In contrast, if the reversion rate is large relative to death and recovery rates, (4) demonstrates that reversion can have a substantial adverse effect on the performance of the transmissible vaccine (Figure 2). This implies that, all else being equal, genetically unstable transmissible vaccines that generate short‐lived infections (i.e., large recovery rate, γV) will be more effective than those that generate long‐term infections from which the host recovers only very slowly (i.e., small recovery rate, γV). The reason the rate of recovery matters, of course, is that long‐lived infections offer substantially greater scope for reversion to vector and thus may undermine the effectiveness of genetically unstable transmissible vaccines.
When cross‐immunity between vector and vaccine exists, identifying conditions under which a transmissible vaccine protects a population from pathogen invasion becomes considerably more complex (Appendix 2). Consequently, although we successfully solved for the critical level of direct vaccination required to prevent pathogen invasion, the expression becomes unwieldy. Instead, we report the key results gleaned from numerical investigations. Plotting the relative performance of a transmissible vaccine as a function of its basic reproductive number, R0,V, and reversion rate to vector, u, demonstrates that any cross‐immunity between vector and vaccine substantially reduces the scope for a transmissible vaccine to outperform a traditional vaccine (Figure 3, compare to Figure 2). This result generalizes previous work (Basinski et al., 2018) by showing that the rate of reversion to vector plays an important role. Specifically, in the presence of cross‐immunity, even rates of reversion as low as 1.5×10-2day-1 (one reversion every 66.7 days, on average), can cause a highly transmissible vaccine to be outperformed by a conventional and directly administered vaccine (Figure 3). Here too, we find that, all else being equal, transmissible vaccines with a rapid host recovery rate are more effective than those with a slow recovery rate. The benefit of rapid host recovery is, once again, the reduction in opportunities for within‐host evolution to cause reversion of genetically unstable transmissible vaccines and the production of insert‐free vector with which the vaccine must effectively compete. These results demonstrate that when cross‐immunity between vector and vaccine exists, the development of effective transmissible vaccines will depend on engineering highly stable recombinant vector vaccines with low rates of reversion to vector.
In the absence of the pathogen and without cross‐immunity between vector and vaccine, the only limit to the spread of a recombinant vector transmissible vaccine is reversion. In Appendix 3, we show that a recombinant vector transmissible vaccine will ultimately be displaced by vector anytime the following condition holds:(5)u>(R0,V-1)(d+γV)
Thus, the more transmissible the vaccine (increasing values of R0,V), the greater the rate of reversion must be for the vaccine to be self‐extinguishing (Figure 4). Because these conditions are in direct opposition to those that increase the performance of a transmissible vaccine, an effective yet self‐extinguishing transmissible vaccine must walk a tightrope between having a low enough reversion rate to be effective against the pathogen and yet a high enough reversion rate to self‐extinguish once direct vaccination ceases. Later, we will explore the scope for a transmissible vaccine to navigate this tightrope using stochastic simulations.
In the presence of complete cross‐immunity, both reversion and competition with viral vector act in opposition to the spread of a transmissible vaccine. Consequently, results derived in Appendix 4 demonstrate that the only condition for such a vaccine to be self‐extinguishing is that reversion occurs. Thus, even though we have ignored potential costs of carrying genetic cargo, the presence of cross‐immunity guarantees that even a slight rate of reversion from vaccine to vector tips the balance in favor of vector and guarantees the ultimate extinction of the transmissible vaccine. This process may, however, be slow if rates of reversion are not appreciable.
In the absence of cross‐immunity, our results show that a transmissible vaccine can be an effective tool for eradicating/eliminating an endemic pathogen even when significant reversion occurs (Figure 5). At the same time, however, our results show that for such a vaccine to self‐extinguish, reversion must increase in proportion to the vaccine R0,V. This sets up a conundrum where the better able the vaccine is to immunologically protect against the pathogen, the harder it is for the vaccine to self‐extinguish. We investigated the scope for resolving this conflict by identifying parameter combinations that allowed the vaccine to first eradicate the pathogen and then subsequently self‐extinguish (Figure 5). This analysis confirmed the challenge of engineering an effective, yet self‐extinguishing, transmissible vaccine and demonstrates that reversion rate, u, and vaccine/vector basic reproductive number, R0,V, must fall within a narrow band of combinations (Figure 5). In addition, all else being equal, as the recovery rate (γV) increases, the range of suitable parameter combinations also increases. Thus, stochastic simulations support the deterministic results in demonstrating that developing an effective, yet self‐extinguishing, transmissible vaccine in the absence of cross‐immunity is theoretically possible but requires challenging engineering and reliable estimates of key vaccine parameters.
Stochastic simulations demonstrate that cross‐immunity between vector and vaccine reduces the scope for pathogen eradication but has little overall impact on opportunities for designing an effective and self‐extinguishing transmissible vaccine (Figure 6). The reason is that, although cross‐immunity makes pathogen eradication more challenging, it practically guarantees that a transmissible vaccine self‐extinguishes from competition with vector, although this process may be slow when rates of reversion are not appreciable. On balance, then, cross‐immunity does little to reduce opportunities for designing an effective, self‐extinguishing, vaccine. Cross‐immunity does, however, affect the parameter combinations that enable success, requiring increased transmission rates and reduced reversion rates (to see this, compare the bottom rows of Figures 5 and 6). Just as in the absence of cross‐immunity, the scope for engineering an effective and self‐extinguishing transmissible vaccine is substantially greater when recovery from vector/vaccine infection is relatively rapid (i.e., γV is relatively large). Also, as we saw before, successful engineering will require that key parameters—such as rates of reversion and transmission—can be accurately measured and finely tuned.
A straightforward approach to estimating u for a recombinant vector vaccine is through replicated serial passage experiments (Figure 7). A possible design would inoculate replicate animals with intact vaccine. These generation‐0 animals would be housed (individually) with uninfected animals and their status monitored. When uninfected individuals became infected with vaccine (generation‐1), they would each be housed with a new, uninfected individual (generation‐2), who is then monitored. A line would be terminated if an uninfected individual either remained uninfected beyond the period of its partner's infectiousness or became infected with revertant only. Individuals would be scored for their infection status (also observing individuals infected with vaccine for conversion to revertant). Instead of relying on natural infection, this process could also be carried out by direct transfer of virus from the infected to the uninfected individual, as suggested in the figure, although such a design faces many decisions that could affect the rate of reversion (e.g., when to manually transmit, how much virus to transmit, which tissues to inoculate).
The experimental design presented above allows the rate of reversion to be estimated using maximum likelihood. We note that any known design could be subjected to its own likelihood analysis, and ours was chosen merely to keep the illustration tractable. The data required are the fraction of the initial lines still carrying vaccine at each point in time, adjusted to exclude lines in which no transmission occurred. This approach neglects issues such as viral polymorphism (or dichotomizes it). The probability that a lineage carries intact vaccine at time t in the experiment is given by:(6)PV=Exp[-ut]
where t is the number of days since the experiment began and all individuals were infected with intact vaccine at the start of the experiment. The probability of observing X lineages with vaccine given a total of N replicate lineages is then given by:(7)L=NXPVX(1-PV)N-X
and the maximum likelihood solution for the reversion rate is given by:(8)u^=Log[nX]t
If PCR and/or serological tests have been conducted at multiple times over the course of the experiment, more refined estimates of the reversion rate can be achieved by integrating this information. Specifically, if N1, N2, …, Nτ lineages have been assayed on days, t1, t2, … tτ, and X1, X2, …, Xτ of these lineages found to be PCR and/or serologically positive for the insert, the likelihood function is:(9)L=∏i=1τNiXiPVXi(1-PV)Ni-Xi
Numerically maximizing this function, or the equivalent log‐likelihood expression, with respect to μ yields an estimate for the key reversion rate parameter of our model.
Our goal has been to investigate the consequences of transmissible vaccine instability on vaccine efficacy and fate. We have focused on recombinant vector vaccines, for which instability is the loss or downregulation of an antigenic insert and loss of vaccine function. Our results demonstrate that recombinant vector vaccines can remain effective, even when genetically unstable and prone to reversion to insert‐free vector. Not surprisingly, this is particularly true for transmissible vaccines that experience little cross‐immunity with the viral vector. In addition to confirming the importance of cross‐immunity, our results show that, all else being equal, those vaccines that transmit rapidly and generate only short‐lived infection will be the most tolerant to genetic instability. Short‐lived infections are favorable because they reduce opportunities for mutation and strain selection within hosts to increase the abundance of revertant vaccine.
In addition to demonstrating that transmissible vaccines can be robust to genetic instability, our results suggest that it may be possible to capitalize on this instability to develop self‐extinguishing transmissible vaccines. The most immediate reason for ensuring that transmissible vaccines self‐extinguish is for regulatory reasons. In this respect, deletion of the insert would restore the vaccine to the status of viral vector, an entity that may be naturally circulating in the wild population. Fortunately, deletion is also the process most easily controlled by engineering. For example, deletions are well known to occur between direct repeats in DNA (Cunningham et al., 1997; Springman, Molineux, Duong, Bull, & Bull, 2012), and modification or elimination of those repeats reduces the spontaneous rate of deletions (Sleight, Bartley, Lieviant, & Sauro, 2010). Genome engineering may also afford the possibility of designing accelerating rates of genomic instability. Our model assumed a constant rate of decay to revertant; a rate that accelerated over time would have many advantages. Such methods are not obviously ready for implementation, but they are at least suggested by “counting mechanisms” that have been employed in bacteria (reviewed in Bull & Barrick, 2017).
Our study contributes to an increasing awareness of the many issues facing the choice of an appropriate vector for a transmissible recombinant vector vaccine. In most cases, the choice of a vector may be based on considerations that lie outside model results, and the model results will then inform the possibilities and avenues for success. Consider cytomegalovirus (CMV), a vector currently being used in the development of transmissible vaccines targeting Ebola and Lassa fever (Marzi et al., 2016; Murphy et al., 2016; Tsuda et al., 2011, 2015). CMV appears promising because of its high level of species specificity, and ability to readily reinfect previously infected hosts (Murphy et al., 2016), a property shown to be critically important here, and in a previous study (Basinski et al., 2018). In contrast, our results also illuminate a potential weakness of CMV, which tends to generate long‐lived infections that our results suggest increase opportunities for vaccine reversion. Ultimately, a rigorous assessment of vector quality will require robust estimates for key parameters such as transmission rates and rates of reversion to vector, something that should be a central focus of ongoing efforts to engineer successful transmissible vaccines.
As with any model, ours make simplifying assumptions that may influence our conclusions. One important assumption is that reversion from vaccine to vector has no impact on rates of transmission, despite the clear reasons to expect greater rates of vector transmission after the genetic cargo has been unloaded. Although we did not explicitly model this scenario, we expect doing so would support our current results. For instance, if the vector transmits more rapidly than the vaccine, we expect cross‐immunity to become even more important and the efficacy of a transmissible vaccine to be further reduced. As a consequence, the difference between vectors that generate cross‐immunity and those that do not would become even more significant. Another important assumption of our model is that it is possible to directly vaccinate newborn animals and that these newborn animals have the same rate of transmission as adult animals. If recovery from vaccine infection is rapid and newborn animals have limited encounters with the population at large, this could substantially limit the efficacy of a transmissible vaccine. Evaluating how this important assumption influences our results will require more complex models that explicitly integrate age structure. Finally, our modeling framework focuses on a single well‐mixed population and thus ignores potential impacts of spatial heterogeneity (Basinski, Nuismer, & Remien, 2019) and population structure (Varrelman, Basinski, Remien, & Nuismer, 2019).
As a whole, our results suggest transmissible vaccines may be relatively robust to modest levels of genetic instability, particularly in cases where cross‐immunity between vector and vaccine is weak. It may also prove possible to capitalize on genetic instability to develop transmissible vaccines that are both effective and self‐extinguishing. Identifying the quantitative impact transmissible vaccines are likely to have on real pathogen populations, however, will require considerable progress in estimating key parameters such as vector transmission rates, recovery rates, and rates of reversion to insert‐free vector. Only when reliable estimates become available for these parameters will it become possible to critically evaluate the promise of various vectors and the scope for designing effective and self‐extinguishing vaccines.
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