Infection dynamics of pandemic IAV

We construct a minimal model to perform scenario analyses for assessing the potential impact of CTL-inducing vaccines in a static population with both pre-existing cellular and humoral immunity to a pandemic virus which has structure as shown in Fig 1. In our model CTL-inducing vaccines reduce the potential infectiousness of vaccinated hosts in a manner that depends on pre-existing host immunity.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Model structure.

Susceptible hosts are divided into 4 strata (labelled by i) depending on their prior influenza experience and vaccination status. Susceptible hosts S_i become exposed (E_i) at a rate proportional to β_f, become infectious (I_i) with Erlang distributed waiting time with rate parameter γ = 1/(1.3 days) and recover (R_i) at a rate ν = 1/(1.6 days). Dashed lines indicate the vaccination of hosts. Note we assume that vaccines do not alter the infectiousness of already exposed hosts (although this distinction is of little consequence if vaccination occurs very early in a pandemic). We allow for the possibility of strain-specific antibody to the pandemic strain by assuming that some (experienced) hosts begin in the recovered state R₃. We assume infected-acquired immunity is maintained over the course of the simulation, however in practice as immunity wanes recovered hosts who were originally naïve migrate to the appropriate experienced susceptible state (R₁ → R₄, R₂ → R₃).

https://doi.org/10.1371/journal.pone.0120138.g001

Our model has 4 main classes of hosts, each occupying an SEIR stratum; vaccinated naïve (i = 1), unvaccinated naïve (i = 2), unvaccinated experienced (i = 3), and vaccinated experienced (i = 4). Susceptible hosts become exposed at a rate governed by β_f and move through a latent state E (implemented using the method of stages to provide Erlang-distributed waiting times from contact to infection [53, 54]). We assume that exposed hosts become infectious I on a time-scale of γ ≡ 1/T_e = 1/(1.3 days) (in keeping with recent estimates of the latency period [55, 56]), and recover to R at a rate ν ≡ 1/T_i = 1/(1.6 days), as described below: (1) where ϵ_N, ϵ, ϵ_E, ∈ [0, 1] respectively denote the infectiousness of vaccinated naïve, unvaccinated experienced and vaccinated experienced hosts relative to unvaccinated naïve hosts. Variables are expressed in numbers of hosts unless otherwise specified. Our choice for T_e and T_i yields a generation time between successive cases of 2.9 days, consistent with average estimates from pH1N12009 surveillance data [57–59], however our results are not altered when adopting other plausible choices for T_e and T_i.

We assume that a fraction f_E of hosts are “influenza-experienced”; having had a previous infection with IAV that confers cross-reactive cellular, and potentially also cross-reactive humoral, immunity to the pandemic virus. The remaining hosts are denoted “influenza-naïve”. The strength of the cellular immunity amongst influenza-experienced hosts ϵ and the prevalence of the humoral immunity amongst influenza-experienced hosts are specified independently of f_E (see below). With the simplifying assumption that lifetime risk of infection increases with age, our choice of f_E = 0.8 roughly translates to assuming that hosts older than 15 have had an infection with IAV (assuming age-demographics for an industrialised country such as Australia, see e.g. http://www.abs.gov.au/). Alternate values for f_E are explored in a sensitivity analysis. The population size N is nominally chosen to be 1 million.

We explore results assuming homogeneous/random mixing (m_NN = m_EE = m_NE = m_EN = 1) or weakly assortative mixing with m_EE = 0.7, m_NN = 1.4, m_EN = m_NE = 1. The latter choice mimics the increased contact rate between younger hosts and between adults and younger hosts seen in survey data [60, 61].

Vaccination

In the absence of firm knowledge of the immunological determinants of host response to a CTL-inducing vaccine, and the epidemiology associated with CTL-immunity, we explore a range of assumptions for prior immunity and vaccine action. In particular, we consider a scenario in which the population has no prior cellular or humoral immunity (A). Such an assumption is likely appropriate if the pandemic strain is of novel subtype and if influenza-specific T-cells commonly found in the population are alone insufficient to suppress transmission from infected hosts (perhaps because elevated levels of effector T cells are required [20]). We also consider three scenarios (B–D) in which influenza-experienced hosts have pre-existing cellular, and perhaps also humoral/antibody, immunity. In scenarios B and C we assume that influenza-experienced hosts have CTL-mediated protection resulting in infectiousness that is 50 per cent that of naïve hosts (ϵ = 0.5), but consider alternative vaccine efficacy assumptions in experienced hosts between the two scenarios (see below). Such protection may reflect the distribution of effective cellular immunity if the influenza-specific T cells found in most adults [12, 21–23] reduce viral shedding. The fourth scenario (D) is motivated by the emergence of H3N2v—a virus with HA protein recognised by antibodies in many adult hosts (McVernon, CDC conference, 2013)—and assigns neutralising antibody to 50 per cent of influenza-experienced hosts in addition to their reduced infectiousness due to cellular immunity (ϵ = 0.5).

Initially all states are empty except for S₂ = (1 − f_E)N and S₃ = f_E N (Scenarios A–C). Hosts with pre-pandemic sterilising immunity begin in the compartment R₃ in our model, yielding initial conditions S₂ = (1 − f_E)N, S₃ = f_E N/2 and R₃ = f_E N/2 for scenario D. Variations on these scenarios are explored in the sensitivity analysis.

We denote the infectiousness of vaccinated naïve hosts relative to unvaccinated naïve hosts ϵ_v. In scenario A, when there is no pre-pandemic immunity, the infectiousness of all vaccinated hosts is uniform. In scenario B we consider a ‘saturating’ vaccine that may not boost existing CTL responses (ϵ_N = ϵ_v, ϵ_E = min(ϵ, ϵ_v)). Such vaccine action may be representative of the action of live influenza vaccines able to induce T-cell responses in children more readily than in adults [39]. In scenarios C and D we consider the impact of a second class of vaccine; a ‘boosting’ vaccine that enhances protection against transmission in experienced hosts who already have naturally acquired CTL protection by the same factor as for naïve hosts (i.e. ϵ_N = ϵ_v, ϵ_E = ϵϵ_v). Viral vector vaccines that show promising results in adults may have such an action if they prove efficacious in children. Lipopeptide vaccines may also have the potential to boost CTL immunity in hosts with a range of pre-existing naïve and memory CTL pools, depending on their design [20]. Table 1 summarises the scenarios A–D examined in the main text.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Scenarios.

The infectiousness of vaccinated and/or experienced hosts (relative to unvaccinated naïve hosts) for the four scenarios A–D presented in the main text. ϵ_v is a free parameter that is set to determine the infectiousness of vaccinated naïve hosts relative to unvaccinated naïve hosts.

https://doi.org/10.1371/journal.pone.0120138.t001

For simplicity we assume that vaccine protection lasts for the duration of the simulation. We explore rapid vaccine distribution to the general population early in the pandemic (with baseline assumption that vaccines are distributed over 10 days) at a range of coverage levels, or pre-emptive targeted distribution of a stockpile allowing 50 per cent coverage. As vaccines inducing T cell responses are still in the design phase, we explore the full range of possible values for ϵ_v ([0, 1]). This parameter can be considered to subsume both ‘uptake’ (vaccinated proportion) and ‘take’ (effectively immunised proportion) given the anticipation of only partial population coverage, resulting from HLA class restriction of CTL epitopes.

Effective reproduction number and the attack rate

The value of the basic reproduction number R₀—indicating the average number of transmitted infections per infected host—expected for future pandemic outbreaks is uncertain. Inferences using mortality and morbidity data from the 1918 Spanish influenza pandemic suggest that R₀ may be as high as 4–6 [62]. The measured effective reproduction number for that pandemic—a composite parameter recognising the constraining influence of the underlying immune profile, social mixing patterns and variations in surveillance strategies—was estimated to be much lower, of order 1.3–3 [63]. Estimates of the effective reproduction number for pH1N12009 [64], and the first wave of the 1968 pandemic [65], also range between 1 and 2.

We consider a pandemic virus that at pandemic onset and prior to vaccination spreads at a moderate rate R_eff = 2. At the time of emergence of a pandemic virus, the existing immune status of a given population is unknown, allowing estimation of R_eff but not R₀ from early observations of the epidemic growth rate [66]. For this reason, in our main analysis we have constrained all studied simulations to have a uniform R_eff = 2 prior to intervention, enabling us to consider the influence of underlying prior immunity on vaccine impact for epidemics that may otherwise appear the same. We explore more severe pandemic scenarios, and a scenario in which the final size of the epidemic, rather than the initial growth rate, is held fixed in the sensitivity analysis. R_eff depends on the population susceptibility profile (including ϵ and f_E) and is the maximum eigenvalue, M, of the matrix constructed by multiplying each row i of β_ij (Equation 1) by S_i(t). In scenario A the absence of any pre-pandemic immunity renders the basic and effective reproduction numbers equal (i.e. R₀ = R_eff). To fix R_eff between scenarios the factor b_f must vary. If there is pre-existing cellular or humoral immunity, R₀>R_eff and β_f is higher than for a scenario without prior immunity. Assuming homogeneous mixing β_f = R_eff/(NT_i) for scenario A, β_f = 5R_eff/(3NT_i) for scenarios B & C, and β_f = 5R_eff/(2NT_i) for scenario D at baseline (i.e. unimpeded by vaccination).

The proportion of the population infected over the course of an outbreak is known as the ‘final epidemic size’ or ‘attack rate’ (despite not being a ‘rate’). We adopt the latter terminology here. We evaluate it numerically as lim_{t → ∞}∑_i R_i(t) or equivalently, $\nu {\sum }_i{\int }_0^{\infty }{I}_i(t)dt$.

Antigenic drift

Changes in the pandemic virus may have been responsible for the increased severity of the second wave of the 1968–9 H3N2 pandemic [67]. Changes in the dominant circulating virus between successive waves of pH1N12009, although not antigenically significant, were also noted [68]. Vaccination campaigns, by altering the immune landscape, have the potential to accelerate, or at least influence, IAV evolution. Modelling frameworks enabling estimation or prediction for the propensity for viral evolution during an epidemic are thus valuable. Invasion by a phenotypically novel variant is an inherently stochastic process more likely to occur in the genetic bottleneck between epidemic waves [69] which we cannot simulate in our single strain deterministic model. However we may estimate the opportunity for generation of new antigenic types and the selection advantage they may be afforded.

To estimate the opportunity for antigenic drift, we assume that each infectious host in each stratum I_i has the potential to transmit a new variant. We calculate the “drift opportunity” P_emg—the cumulative opportunity for drift variants to emerge over the course of the epidemic—by integrating over all infections as below: (2) where t_end corresponds to the resolution of the epidemic. Note that we only report dimensionless values of P_emg that are normalised by the value for the same epidemic without intervention. P_emg > 1 is possible and indicates an epidemic in which drift opportunity under intervention was greater than than in the absence of intervention. The non-linear dependence on time in Equation (2) which allows for P_emg > 1 is motivated by results from theoretical models for antigenic drift suggesting that new variants may be more likely to circulate later after introduction of the initial strain [70, 71]. The adopted power-law dependence on time is a phenomenological fit to the rate of antigenic cluster turnover for H3N2 from Koelle et al. [47]. We have assumed that t_e is the time since the cumulative incidence reaches 1 (host) in our deterministic model.

The factor g_0,i in Equation (2) is the per infection rate of emergence of new variants for hosts in stratum i. Arinaminpathy et al. assume that the per infection rate generating new variants depends only on cluster age [46] (i.e. g_0,i = 1). However, the emergence and thus transmission of variants from a host may be more common when infections are prolonged and viral replication occurs in the presence of sterilising or cross-reactive antibody [72, 73]. Prime-challenge experiments in macaques indicate that priming with seasonal H1N1 viruses 4 months prior to challenge with pH1N12009 enables CTL responses that clear the infection before appearance of neutralising antibody [74], suggesting that infections in vaccinated hosts with a readily primed CTL response may be associated with a significantly lower probability of selecting and transmitting antigenically novel variants. We thus explore 3 forms for the contribution of each infection to the overall probability of antigenic emergence: (i) g_0,i = 1 (per infection rate of emergence of new variants independent of vaccination and pre-pandemic immune status), (ii) g_0,i = ϵ_i (per infection rate of emergence of new variants proportional to net viral load/host infectiousness), and (iii) the distribution g_0,1 = g_0,2 = g_0,3 = ϵ_i, g_0,4 = 0 (per infection contribution equal for all hosts except no contribution from CTL-vaccinated experienced hosts). Here ϵ_i is the infectiousness of hosts in the ith stratum. It is also possible in principle that CTL responses may enhance selection of novel variants, in which case scenarios with g_0,i > 1 may be justified. Such a possibility is not explored in this work.

Antigenic variants may have mutations that confer increased virulence/transmissibility and/or escape recognition of antibodies to the original pandemic virus and thus facilitate the process of antigenic drift. We focus on the selective advantage of the latter type of antigenic variant, assuming that the intrinsic transmissibility is unchanged from that of the original pandemic strain. The selective advantage of a new variant is largely governed by the ratio of effective reproduction numbers for the replacing and resident strains [75]. To gauge the probability that an antigenic variant that emerged during the pandemic (with probability proportional to our calculated “drift opportunity”) is selected, we consider this ratio at the conclusion of the pandemic. The effective reproduction number of the emerging strain R_eff,new is calculated assuming that it escapes all antibody-mediated immunity remnant after resolution of the initial pandemic wave. The ratio R_eff,new/R_eff naturally increases with the prevalence of immunity to the resident pandemic strain.

Mitigating potential of CTL-inducing vaccines

Our predictions for the attack rate as a function of CTL-inducing vaccine coverage vary significantly with underlying population immunity and vaccine action for pandemic scenarios A–D with the same initial growth rate. The mitigating potential is very similar for homogeneous and assortative mixing scenarios when vaccines are distributed uniformly amongst the population (see Fig 2 and S1 Fig).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 2. Attack rate with coverage for scenarios A-D.

Predicted attack rates for four different pandemic and vaccine action scenarios as a function of general population coverage with a CTL-inducing vaccine. In each panel the solid line corresponds to assumptions of relative infectiousness in vaccinated and unvaccinated naïve hosts of ϵ_v = 0.25, with dashed and dotted lines corresponding to ϵ_v = 0.5 and 0.75 respectively. Scenario A captures a population without pre-existing CTL-mediated immunity to the pandemic strain. In scenarios B and C, 80 per cent of the population have pre-existing CTL-mediated immunity (f_E = 0.8) suppressing infectiousness by 50 per cent (ϵ = 0.5), with vaccine action saturating (B) or boosting (C). Scenario D is a modification of scenario C that assumes 50 per cent of those with naturally acquired CTL immunity also have cross-reactive protective antibody.

https://doi.org/10.1371/journal.pone.0120138.g002

In this subsection we focus our discussion on the homogeneous mixing case (Fig 2) but highlight interesting differences to the assortative mixing case. In the absence of any prior immunity (scenario A) the impact of vaccination is simple to predict (see [46]). The highest efficacy vaccine considered, which suppresses the infectiousness of vaccinated naïve hosts to ϵ_v = 0.25 relative to unvaccinated naïve hosts, can mitigate the pandemic with 65 per cent coverage. Attack rates are approximately halved to 40 per cent if coverage with such a vaccine is 50 per cent.

For scenarios in which there is only prior cellular immunity to the pandemic strain (B & C) baseline attack rates are equal to that for scenario A for fixed R_eff. Note that this is only strictly true when mixing is homogeneous as the introduction of assortative mixing influences the value of R₀ for fixed R_eff, however the variation between scenarios A–C is very small for our choice of assortative mixing (see S1 Fig). In scenario B, unless the ability of the vaccine to suppress infectiousness is superior to the suppression arising due to naturally acquired pre-existing CTL immunity, even high levels of vaccine coverage will not significantly reduce the attack rate. In particular, attack rates would still be above 70 per cent if coverage of 50 per cent were achieved for vaccines with ϵ_v ≳ 0.5. The benefit of widespread vaccination in scenario B is only mildly inferior to that for scenario A when ϵ_v = 0.25. In contrast, if the vaccine can further suppress the infectiousness of vaccinated experienced hosts (scenario C), predictions for vaccine impact are more promising. Indeed the mitigating impact of vaccination campaigns achievable in scenario A is recovered.

In scenario D the overall attack rate is lower than scenarios A–C despite assuming the same initial growth rate, as the size of the cohort without protective antibodies is limited to 0.6N. Baseline attack rates amongst the naïve subpopulation however are equivalent to those in scenarios A–C when mixing is random (S2 Fig). As a larger portion of the initial growth rate is driven by the naïve hosts, such individuals are preferentially infected driving R_eff below 1 more rapidly than in the other scenarios considered. The accuracy of predictions for the attack rate from early estimates of R_eff is thus clearly contingent on understanding underlying population heterogeneities in mixing and immunity. Despite the lower attack rate in scenario D, overall attack rates decline more slowly with coverage than for the other scenarios that assume a boosting vaccine (i.e. scenarios A & C, see Fig 2). Slightly higher coverage with the most efficacious vaccine considered (ϵ_v = 0.25) is required to halt the pandemic than for scenarios A or C, as many vaccines are ‘wasted’ preventing transmission from hosts who are not susceptible (Fig 2). Distributing CTL-inducing vaccines to the general population will have greater power to reduce epidemic spread when there is little existing neutralising cross-reactive antibody to the pandemic strain.

Distribution strategies for CTL-inducing vaccines

We explore the impact of distributing vaccines to varying proportions of naïve and experienced hosts assuming both homogeneous and assortative mixing for scenarios B–D (i.e. scenarios which assume heterogeneous pre-pandemic immunity). The impact of this targeted distribution when mixing is homogeneous is depicted in Fig 3. The advantage of distributing vaccines to naïve hosts in scenario B is intuitive when ϵ_v ≳ ϵ and the vaccine cannot reduce the potential infectiousness of experienced hosts. However, reduced attack rates when targeting naïve hosts are apparent even when the vaccine suppresses the transmission potential by the same factor in naïve and experienced hosts (scenarios C & D). Assuming R_eff = 2 and a vaccine stockpile sufficient for 50 per cent population coverage, distribution of a vaccine that completely blocks transmission (ϵ_v = 0) won’t halt population spread unless ≳50 per cent of naïve hosts are vaccinated in scenarios B-D (Fig 3). It is important to note that the preference for vaccinating naïve hosts in Fig 3 is purely driven by their larger potential infectiousness. The optimal efficiency of such ‘equalising’ vaccine strategies have also been discussed elsewhere (see, for example, [76]). As a result, the benefit of targeting naïve hosts (i.e. small values of “exp coverage”) shows a similar trend across scenarios B–D (Fig 3), but with some important differences. In particular, such targeted strategies enable mitigation with poorer performing, but still efficacious (ϵ_v < 1), vaccines.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 3. Attack rates for targeted vaccination in Scenario C.

Epidemic attack rates for targeted distribution of a vaccine stockpile sufficient for 50 per cent coverage. For all epidemics the initial effective reproduction number in the absence of vaccination is fixed at 2. The axis labelled “exp coverage” denotes coverage in the experienced population and ϵ_v is the relative infectiousness of vaccinated and unvaccinated naïve hosts. The minimum plotted value of “exp coverage” indicates full coverage in the naïve population with the remainder given to experienced hosts, the maximum plotted value is for a scenario in which all vaccines are given to experienced hosts, and a value of 0.5 indicates equal coverage in naïve and experienced hosts (i.e. general population distribution). Panels represent estimates for different pre-pandemic immunity and vaccine action scenarios; 80 per cent of the population with naturally acquired CTL-mediated immunity (f_E = 0.8) and saturating vaccine action (scenario B), the same population with a vaccine that boosts protection in all hosts (scenario C), a population in which 50 per cent of those with naturally acquired CTL responses also have protective antibody to the pandemic strain and vaccine action is again boosting (scenario D). The strength of naturally acquired CTL-mediated immunity is set to ϵ = 0.5.

https://doi.org/10.1371/journal.pone.0120138.g003

When assuming random mixing, targeted vaccination in scenarios B & C does not alter the relative attack rates in naïve and experienced hosts, as all hosts are equally susceptible. However targeting naïve hosts in scenario D can markedly reduce the attack rate in this sub-population; the attack rate could potentially be constrained to below 10 per cent if ϵ_v ⪅ 0.35. In contrast, targeting experienced hosts in scenario D would enable widespread infection of naïve hosts with sub-population attack rates in excess of 50 per cent if ϵ_v ≳ 0.5 (data not shown). Adopting assortative mixing (as described earlier) instead of homogeneous mixing also increases the predicted benefit of reducing the coverage amongst influenza-experienced hosts for low to intermediate values of ϵ_v (S3 and S4 Figs).

CTL-inducing vaccines and antigenic drift

For our baseline parameter assumptions, with R_eff = 2, the drift opportunity P_emg decreases with coverage and is necessarily null when the pandemic is mitigated. However, when the per infection probability of the emergence of variants is constant (i.e. g_0,i = 1)—as assumed in previously published work [46]—the decline in drift opportunity with increased coverage (upper panels, Fig 4) is slower than that predicted for the attack rate (Fig 2). As a consequence drift opportunity is barely reduced even for full population coverage with a lower efficacy vaccine (ϵ_v = 0.75) for all scenarios, and remains approximately equal to that for an unimpeded pandemic in scenario B when ϵ_v ≳ 0.5. Assuming a boosting vaccine and no strain-specific humoral immunity (scenario C), 50 per cent coverage with a vaccine reducing the infectiousness of naïve hosts by ϵ_v = 0.25 reduces the drift opportunity to approximately 75 per cent of that for an unimpeded epidemic (Fig 4). Drift opportunity is minimised when vaccines are distributed to naïve hosts, mirroring the trends seen in the attack rate (left panel, Fig 3).

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 4. Drift opportunity with coverage for scenarios A-D.

Upper panels: drift opportunity relative to an unimpeded epidemic as a function of general population coverage for four different pandemic and vaccine action scenarios assuming R_eff = 2, homogeneous mixing and g_0,i = 1. Lower panels: The ratio of effective reproduction numbers of antigenically novel and resident pandemic variants. The grey line indicates a ratio of unity. In each panel the solid line indicates results assuming that the relative infectiousness in vaccinated naïve and naïve hosts is ϵ_v = 0.25, with dashed and dotted lines ϵ_v = 0.5 and 0.75 respectively.

https://doi.org/10.1371/journal.pone.0120138.g004

We focus on exploring variations in the achievable reduction in drift opportunity with the choice of g_0,i for fixed vaccine coverage of 50 per cent in scenario C with homogeneous mixing (Fig 5). Reductions in drift opportunity are naturally larger when the per infection probability of emergence of antigenic variants scales with host infectiousness (g_0,i = ϵ_i) than if this per infection rate is uniform (g_0,i = 1). General population vaccination achieving 50 per cent coverage (i.e. exp coverage = 0.5) using a vaccine with ϵ_v = 0.25 can reduce drift opportunity to approximately 47 per cent of that for an unimpeded epidemic in this situation (see Fig 5). As for the attack rate, drift opportunity is minimised when vaccines are distributed to naïve hosts, despite the very low infectiousness of vaccinated experienced hosts when the vaccine has a boosting action.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 5. Drift opportunity in scenario C.

Drift opportunity for scenario C with targeted distribution of a vaccine stockpile sufficient for 50 per cent coverage and assuming that pre-vaccination R_eff = 2. The axis labelled ϵ_v indicates the relative infectiousness of vaccinated and unvaccinated naïve hosts and “exp coverage” indicates the fractional vaccine coverage in experienced hosts (vaccine distribution is random when exp coverage is 0.5). Each panel corresponds to a different assumption regarding the form for the per infection rate of antigenic emergence g_0,i; equal probability per infection (left), proportional to host infectiousness (middle), and zero for vaccinated hosts with existing CTL protection (right). The vertical axis show the probability of emergence P_emg of an antigenically novel variant over the course of the epidemic relative to the same scenario without intervention.

https://doi.org/10.1371/journal.pone.0120138.g005

If CTL vaccination completely suppresses the per infection probability of emergence of variants from vaccinated experienced hosts (i.e. g_0,4 = 0, g_0,i = 1 otherwise), then the drift opportunity is further reduced compared to the scenario where g_0,i = ϵ_i for ϵ_v ≳ 0.2 (Fig 5). In contrast to the first two forms for g_0,i discussed, distributing CTL-inducing vaccines to experienced hosts minimises the drift opportunity in scenario C when ϵ_v ≳ 0.25 (Fig 5). In particular, the drift opportunity is approximately 20 percentage points lower when a stockpile allowing 50 per cent coverage for ϵ_v = 0.75 is preferentially administered to experienced rather than naïve hosts. In contrast the attack rate is only 4 percentage points lower (69 per cent compared to 73 per cent) if naïve hosts rather than experienced hosts are targeted. If ϵ_v ⪅ 0.25 the drift opportunity remains more efficiently suppressed by targeting naïve hosts to curtail the epidemic size. This trend holds for our assumed choice of assortative mixing (data not shown). Targeting experienced hosts has similar benefits for suppressing drift opportunity for moderate to high values of ϵ_v in scenario B, but has muted benefit in scenario D due to the smaller contribution of experienced hosts to the overall attack rate (data not shown). Note that for the final choice of g_0,i presented (right panel, Fig 5) we have assumed that even vaccines that don’t reduce overall host infectiousness (ϵ_v = 1) can completely suppress the emergence of new variants in experienced hosts. In practice a threshold vaccine efficacy may be required to generate such an effect.

Our estimate for the selective advantage of an antigenically novel variant circulating at the conclusion of the first pandemic wave R_{eff, new}/R_eff depends on both pre-pandemic immunity and the pandemic attack rate, and thus varies between scenarios and with vaccine coverage (lower panels, Fig 4). In the absence of pre-pandemic neutralising cross-reactive antibody (scenarios A–C), if a vaccination campaign is able to mitigate spread the relative effective reproduction ratios of the (assumed equally transmissible) antigenically novel variant and resident pandemic strain remains unity. If vaccination does not mitigate the pandemic, antigenically novel variants have a distinct advantage that increases with the pandemic attack rate. Although attack rates—and thus the size of the population with acquired immunity—are smaller when there is pre-pandemic antibody mediated immunity in scenario D, the advantage of antigenically novel variants is compounded by this pre-existing immunity. If antigenic escape were to occur in this scenario the new variant will likely displace the original pandemic strain (R_eff,new/R_eff > 2), potentially triggering a second wave of severe infection unconstrained by the cross-reactive antibody that limited the initial wave. If a CTL-inducing vaccine offers truly heterologous protection that suppresses hosts potential to transmit all IAV strains equally, increasing vaccination coverage cannot erase the advantage afforded to antigenically novel strains that emerge in the presence of immunity-driven selective pressures unless they halt almost all transmission thereby rendering P_emg negligible (see also [46]). However, unlike traditional vaccination campaigns which would increase R_eff,new/R_eff even if the pandemic were mitigated, CTL-inducing vaccines do not further enhance the selective pressure for new antigenic variants.

Sensitivity analysis

In the above sections we have explored the sensitivity of expected vaccine impact—as measured by the attack rate and/or drift opportunity—on underlying population immunity, population mixing characteristics and vaccine action. Here we additionally consider the sensitivity of our results to the transmissibility of the pandemic virus, the period of vaccine distribution, and alternate profiles for pre-pandemic population immunity for the homogeneous mixing case.

Study limitations

We have adopted a minimal model to explore the impact of prior immunity and CTL-vaccine action on CTL-inducing vaccination campaign impact. This choice allowed us to explore a broader set of pandemic and vaccination scenarios, including the possibility of heterogeneous pre-pandemic cellular immunity, than explored in previous work [46]. As we model the transmission of a single pandemic IAV strain, and include within-host effects of CTL immunity through stratification of host infectious type, we can only estimate the potential for antigenic drift and strain replacement after a single epidemic wave without assigning this potential a calibrated probability. Population-level IAV circulation may also be influenced by within-host and population mixing effects not considered in our model: Luo et al. suggest that partial protection, by preventing target cell depletion, increases the opportunity for novel viruses to attain higher within-host viral loads [79], and the pattern of immune responses in chains of infection can also influence viral selection [80]. Our model assumes a simple distribution of pre-pandemic cellular and humoral immunity, which likely does not capture all age-cohort dependent trends in immune status. However detailed models for age-structured T cell immunity are difficult to justify given the scarcity of available data on human T cell immunity.

Implications

Our modelling demonstrates that the utility of CTL-inducing vaccine candidates is not guaranteed, and provides insight into the efficacy and distribution strategies required to control pandemic influenza with next-generation CTL-inducing vaccines. In particular we have demonstrated that vaccine impact may hinge on as yet uncharacterised cellular immunity, with vaccination campaigns less likely to be of use if this is common and difficult to boost. However even if CTL-mediated immunity amongst adults is common and can be enhanced with vaccination, the most efficient way to control future pandemics may be to boost CTL immunity in younger hosts, regardless of considerations of enhanced transmission due to contact patterns that result in recommendations of preferential vaccination of children with traditional vaccines [76, 81]. Focusing on developing CTL-inducing vaccines that induce protective responses in hosts with naïve T cell pools may therefore be of particular importance. Only if a CTL-inducing vaccine performs particularly poorly in naïve/unprimed hosts might vaccination campaigns targeting experienced hosts be preferable for reducing the attack rate. Vaccination campaigns that aim to prime naïve T cells will likely have ongoing benefit—enhancing post-pandemic cellular immune responses to all IAV—even if the initial protective immune response triggered by the vaccine wanes over time [20]. However the prevention of senescence of T cell immunity might offer alternative motivation for administering CTL-inducing vaccines to older hosts [43].

We have explored the extent to which the genealogy of the pandemic strain may also limit the impact of CTL-inducing vaccination campaigns. A key determinant of the impact of CTL vaccination campaigns, particularly those aiming to vaccinate adults, will be the coupling of cohorts with boostable CTLs and neutralising antibody. Most human IAVs have their origin in avian variants [82], but viruses with the appropriate receptor specificity are more likely cross-over from swine, and IAV subtypes that circulate widely in swine are also those that circulate as seasonal influenza in humans [83]. As illustrated by the emergence of H3N2v, IAVs at the human-swine interface may be antigenically similar to recently circulating human seasonal IAV, and induce neutralising cross-reactive antibody in many adults that likely supersedes the protection afforded by enhanced CTL responses. Cellular immunity—which likely cannot prevent infection but only suppress transmission—may be of limited relevance for controlling the spread of such a virus. The presence of other heterologous immune responses to the pandemic virus, such as cross-reactive antibodies to sub-dominant epitopes [84], are likewise of lesser consequence if there is sterilising immunity to the immunodominant epitopes. Enhancing cellular immunity is more likely to aid pandemic control when the pandemic virus has an antigenic subtype that has experienced limited circulation in humans (scenarios A–C), such as the avian viruses H5N1 IAV [85] or the recently emerged H7N9 IAV [52]. These insights add to understanding of the role of pre-pandemic cellular and humoral immunity—in concert with host mixing effects—in determining the risk landscape for infection with pandemic viruses.

The influence of CTL-mediated immunity on host propensity to transmit new genetic variants may be an important consideration when designing strategies to minimise the risk of viral drift during a pandemic [67, 68]. We have demonstrated that the influence of CTL-inducing vaccination campaigns on antigenic drift may be greater than suggested by previous modelling work [46]. In contrast to the benefits of targeting children to reduce the attack rate, if CTL-inducing vaccines facilitate rapid clearance in primed hosts, targeting adults may be an efficient way to reduce the drift opportunity when the vaccination campaign does not have the power to significantly curtail the attack rate.

Open questions

There is much scope to enhance our understanding of CTL-immunity and the likely utility of CTL-inducing vaccines by developing mathematical transmission models that incorporate the accumulating insight from immunological and epidemiological studies of the role of cellular immunity in regulating IAV infection in humans. Comprehensive modelling of CTL vaccination impact will require more detailed characterisation of the development and maintenance of memory CTL, the role of memory CTL on influenza infection, and the distribution of this immunity in socially realistic populations. Together with further study of influenza T-cell immunology in animal models, insights from household-based cohort studies or challenge studies will be key for modelling the development and prevalence of functional T cell immunity. Within-host modelling of IAV infection in the presence of CTL responses that can reproduce emerging experimental data will be required to aid understanding of the potential for CTL-inducing vaccines to alter the likelihood that hosts transmit IAV variants. Modelling of IAV circulation and evolution over time-scales longer than a single season that accounts for the development and maintenance of influenza-specific memory CTL will be required to predict the impact of sustained wide-spread CTL-inducing vaccine usage, including the risks and consequences of CTL vaccine escape.

Our results highlight the need for vaccine design to attend to our developing understanding of the ontology and evolution of T cell immunity in humans (e.g. [86]). Epidemiological studies looking for exposure dependent differences between precursor and effector CTL pools, will give insight into whether CTL-inducing vaccines might alter this response to boost ‘sub-dominant’ epitope-specific CTLs and provide protection superior to that triggered by natural infection (akin to scenario C), providing insight into the optimal design and potential efficacy of CTL-inducing vaccines against IAV.

Consideration of the utility of multi-faceted public health responses that use CTL-inducing vaccines to buy time before a strain-specific vaccine can be distributed, and/or use of CTL-inducing vaccines in tangent with traditional anti-viral drugs, are also of interest. In future work we will explore strategies for the optimal use of CTL-inducing vaccines that take into account sociologically important differences in mixing behaviour for adults and children in addition to differences in immunological memory to IAVs.