on 20-Nov-2019 (Wed)

The study by Reich et al. (13) points at an overall degradation of disease forecasts at the 4-wk time horizon, beyond which the average of historical incidences (i.e., a null model) becomes the most reliable option for prediction.

From a public health standpoint, a longer horizon, in the order of 2 mo or more, would be particularly useful to ramp up interventions and adjust hospital surge capacity.

Ideally, even longer timescales should be considered so that the prediction of epidemic intensity (epidemic size) and severity (total number of hospitalizations and deaths) aligns with the vaccine manufacturing process.

Wearing et al. (2005) use analytical methods to show that

(i) ignoring the latent period

or

(ii) making the common assumption of exponentially distributed latent and infectious periods (when including the latent period)

always results in underestimating the basic reproductive ratio of an infection from outbreak data

The 2014–2015 outbreak of Ebola in West Africa serves to highlight both opportunities and challenges in modeling for public health. In the initial phase of this outbreak, real-time estimates of the reproduction number or simple exponential extrapolation (14) allowed short-term predictions of epidemic growth that were used, for example, to plan for necessary bed capacity. Quantitative phylogenetic tools applied to samples from initial victims provided important estimates of the origin of the outbreak (15). Early mechanistic models that explicitly took into account the roles played by different transmission routes or settings were informed by analysis of earlier outbreaks (16, 17).

Hill et al. (2019) amalgamate multiple data sources to calibrate a susceptible-latent-infected-recovered type transmission model for seasonal influenza, incorporating the four main strains and mechanisms linking prior season epidemiological outcomes to immunity at the beginning of the following season.

Data pertaining to nine influenza seasons, starting with the 2009/10 season, informed our estimates for:

• epidemiological processes,
• virological sample positivity,
• vaccine uptake and efficacy attributes, and
• general practitioner influenza-like-illness consultations as reported by the Royal College of General Practitioners (RCGP) Research and Surveillance Centre (RSC).

We performed parameter inference via approximate Bayesian computation to assess strain transmissibility, dependence of present season influenza immunity on prior protection, and variability in the influenza case ascertainment across seasons. This produced reasonable agreement between model and data on the annual strain composition.

Parameter fits indicated that the propagation of immunity from one season to the next is weaker if vaccine derived, compared to natural immunity from infection. Projecting the dynamics forward in time suggests that while historic immunity plays an important role in determining annual strain composition, the variability in vaccine efficacy hampers our ability to make long-term predictions.

Influenza vaccination can offer some protection against seasonal influenza infection for the individual, while contributing to reduced risk of ongoing transmission via establishment of herd immunity [3, 4]. Influenza vaccines are designed to protect against three or four different influenza viruses; two influenza A viruses (an A(H1N1)pdm09 subtype and A(H3N2) subtype) and either one or two influenza B viruses (covering one or both of the B/Yamagata and B/Victoria lineages).

Here, we present a multi-strain, non-age structured, susceptible-latent-infected-recovered (SEIR) type transmission model for influenza incorporating a mechanism to link prior influenza season epidemiological outcomes to immunity at the beginning of the following influenza season. Incorporation of a mechanism for the building and propagation of immunity facilitates investigation of the impact of exposure in the previous influenza season, through natural infection or vaccination, on the disease transmission dynamics and overall disease burden in subsequent years.

Accordingly, we sought insights to aid understanding of the longer-term dynamics of the influenza virus and its interaction with immunity at the population level. In this study, we examine the contribution of the differing sources of immunity propagation between years on seasonal influenza transmission dynamics.

To this end, we amalgamate multiple sources of epidemiological and vaccine data for England covering the last decade, and fit model outcomes to the available longitudinal data of seasonal rates of general practice (GP) consultations for influenza-like-illness (ILI), scaled by virological surveillance information.

We demonstrate that natural infection plays a more prominent role in propagation of immunity to the next influenza season compared to residual vaccine immunity. We conclude by inspecting forward projections under disparate vaccine efficacy assumptions to determine long-term patterns of seasonal influenza infection.

Hill et al. (2019) used data subsequent to the 2009 pandemic for England, and developed a dynamic multi-strain SEIR-type transmission model for seasonal influenza, explicitly incorporating immunity propagation mechanisms between influenza seasons. With a view to minimising the number of independent parameters, we fit a parsimonious mechanistic model to seasonal-level data on strain competition. In spite of the multi-strain complexity and time scale of the study period (six influenza seasons), predictions from the model attain a strong qualitative resemblance (in terms of strain composition and overall quantity of GP consultations) to the empirical subtype data from England.

In the case of finding minimal support for carry over cross-reactivity protection between influenza B lineages (parameter b), we have reported the best parameter fits under the modelling assumptions made. Considered collectively, the inferred parameter fits signify that, at the population level, a combination of transmissibility rates, season-specific ascertainment probabilities and modifications to susceptibility by lineage-specific immunity propagation (parameter a) and within-season vaccination are sufficient to obtain the closest correspondence to the data under the modelling assumptions, without requiring a prominent amount of influenza B cross-reactive immunity propagation. In other words, if there was presence of propagation of protection between influenza B lineages, it was dwarfed by other processes within the biological system.

The effects that consequential increased media coverage of an outbreak have on transmission dynamics can be complex [55], with the perception of the disease conceivably changing among the population [56]. Chiefly in this instance, for those infected and symptomatic the propensity to consult a GP may have been abnormally raised, which would result in an increased ascertainment probability relative to prior influenza seasons.

Spanning our pessimistic to optimistic vaccine efficacy scenarios, Hill et al. (2019) generally attained a model predicted incidence (per influenza season) of 30-50%. With volunteer challenge studies indicating that the majority of those infected by influenza are asymptomatic [57], plus only around 10% of those with ILI thought to consult a GP [58, 59], our model predicted influenza incidence pairs satisfactorily with previous influenza burden estimates covering England [60]. Additionally, influenza burden estimates in the USA (provided by the CDC) covering the 2017/18 and 2018/19 influenza seasons ascribe more than 48.8 million and 37.4-42.9 million influenza associated illnesses respectively, which is in the realms of 10-15% of the national population suffering symptomatic infection [61, 62].

Recent work has found H1 and H3 influenza infection in humans induces neuraminidase-reactive antibodies displaying broad binding activity spanning the entire history of influenza A virus circulation (in humans) [37]; these developments motivate continued work and data acquisition to elicit the timespan over which cross-reactive antibodies (arising from natural influenza infection) may significantly reduce susceptibility to unrelated influenza A subtypes and influenza B lineages.

Hill et al. (2019) assumed the mechanism underpinning propagation of immunity from influenza vaccination in the previous influenza season behaved linearly. We recognise a linear dependency is a strong generalisation. Given the vaccine-induced protection to an influenza virus strongly depends on the level of mismatch of the strain contained in the vaccine and the circulating strain, a vaccine that is very protective in the current influenza season might be ineffective the following year due to the influenza virus undergoing antigenic mutation.

HIll et al. (2019) find that susceptibility in the next influenza season to a given influenza strain type is modulated to the greatest extent through natural infection by that strain type in the current influenza season, with residual vaccine immunity having a lesser role and inconsequential support for carry over type B cross-reactivity.

define a complete epidemiological influenza season to run from week 36 to week 35 of the subsequent calendar year. We chose week 36 (which typically corresponds to the first full week in September) as the start week to match the start of the epidemic with the reopening of schools.

ILI is a medical diagnosis of possible influenza with a set of common symptoms: cough and measured or reported fever >38˚C, with onset within the last 10 days [21]

By scaling the longitudinal data of GP consultations for ILI by the virological surveillance information we garnered an overall estimate of ILI GP consultations attributable to influenza

We computed the circulating strain distribution in each influenza season using publicly available data from FluNet [26], a global web-based tool for influenza virological surveillance, using data for the United Kingdom.

From supplemantary info: "we assumed the fraction of undetermined samples ascribed to eachsubtype/lineage matched the proportions observed for the set of samples where strain-specific information were available"

These computations resulted in seasonal rates of GP consultations attributable to the two influ- enza A subtypes and two influenza B lineages per 100,000 population (Fig 1(a)). Uncertainty distributions for these values were obtained via bootstrapping given the sample sizes for the three components.

For the 2010/11 influenza season onward we collated vaccine uptake information from PHE official statistics [24, 25]. We took age adjusted vaccine efficacy estimates for each historical influenza season (2009/ 2010-2017/2018 inclusive) from publications detailing end-of-season seasonal influenza vaccine effectiveness in the United Kingdom [28–34]. In influenza seasons where equivalent publications were not available, we used mid-season or provisional end-of-season age adjusted vaccine efficacy estimates from PHE reports [35, 36].

There has been substantial variation in vaccine efficacy between influenza seasons and also within influenza seasons across strains, with estimates spanning 23-92% (Table 1). Further, there have been two instances of a mismatch between the vaccine and circulating viruses caus- ing the vaccine to be ineffective (i.e. 0% efficacy) against a particular strain group

Influenza transmission dynamics are highly complex, with many temporal and structural heterogeneities that will influence the precise pattern of recorded infection. Consequently, our aim was to capture the general trends in the data, such as the pattern of high and low infection levels, rather than the precise values for each influenza season. We, therefore, deliberately chose a parsimonious mechanistic modelling framework, without age-structure, to highlight the impact of immunity propagation.

The model takes the form of a deterministic continuous-time set of ordinary differential equations (ODEs), which determines the within-season epidemiological dynamics, and a discrete-time map, informing the propagation of immunity from one influenza season to the next.

Multiple infections per influenza season and/or co-infection events were not permitted. In other words, it was presumed that individuals may only be infected by one strain of influenza virus per influenza season, analogous to natural infection eliciting short-term cross immunity to all other strain types [37].

We obtained weekly time-varying vaccine uptake rates, ν, at the population level by computing a weighted average of the individual age group uptake values, thereby accounting for the popula- tion distribution in each given influenza season. We assumed the rate of vaccination ν to be constant over each weekly period.

The ‘leaky’ vaccine action contrasts with an ‘all-or-nothing’ vaccine assumption, which assumes complete protection to a subset of the vaccinated individuals but no protection in the remainder of vaccinated individuals [38]. Explicitly, under a ‘leaky’ vaccine action with a vaccine efficacy against strain m of α m , the relative susceptibility of the vaccinated group towards strain m is 1 − α m .

Three susceptibility modifying factors of interest were: (i) modified susceptibility to strain m given infection by a strain m type virus the previous influenza season, denoted a; (ii) carry over cross-reactivity protection between influenza B lineages, denoted b (to account for infection with one influenza B virus lineage being potentially beneficial in protecting against subsequent infection with either influenza B virus lineage [39]); (iii) residual strain-specific protection carried over from the prior season influenza vaccine, denoted c m . We mandated that 0 < a,b,c m < 1. We let f(h, m) denote, for those in exposure history group h, the susceptibility to strain m. The collection of ten exposure history groupings and associated strain-specific susceptibilities were consolidated into a single susceptibility array (Fig 2, process B; Fig 3).

we took a pessimis- tic stance by assuming no boosting of the immunity propagation response as a result of dual influenza virus exposure (from both natural infection and vaccination).

In light of there being uncertainty around the precise time scale for which immunity to seasonal influenza viruses may be retained, with individualand population-level models having estimated infection acquired immunity to wane over a timescale of two to ten years [40–42]), we also considered an extended variant of the immunity propagation model component.

In the model extension, we fit an additional parameter (δ) representing the proportion of those who began the influenza season in an exposure history group linked to natural infection (Fig 3: rows 2-5, 7-10), and who were also unexposed to influenza virus during the current season (who at the end of the current influenza season remained susceptible), that retained their pre-existing natural infection acquired immunity. Those keeping immunity arising from natural infection were mapped to the relevant prior infection exposure history group dependent upon current influenza season vaccination status. The remaining proportion (1 − δ) transitioned in the same manner as in the original model, reverting to either the naive exposure history group or vaccinated only exposure history group (Fig. T in S1 Text).

For clarity, we did not introduce a mechanism to confer vaccine-induced immunity beyond one influenza season (i.e. vaccine-induced immunity could be retained for, at most, a single additional influenza season). With the more complex immunity structure, we did not gain noticeable improvements in correspondence of model outputs with the data (relative to fits with a model using the simpler immunity propagation setup).

We assumed exponentially-distributed latent and infectious periods (arising from rates of latency loss and recovery, respectively, being constant). Loss of latency rates γ_1,m were strain-dependent. From Lessler et al. [43], we chose rates corresponding to average latent periods of 1.4 days and 0.6 days for influenza A and influenza B associated strains respectively. Following Cauchemez et al. [44], we set the rate of loss of infectiousness γ₂ = 1/3.8, corresponding to an average infectious period of 3.8 days, independent of strain.

each individual infected by the strain of influenza under consideration had a probability of being ascertainable, i.e. going to the GP, being recorded as having ILI, and having a detectable influenza viral load

Inferred ascertainment probabilities (�), across all influenza seasons, were typically within the range of 0.001-0.006. The highest ascertainment probabilities were found for the recent 2017/18 influenza season, attaining a median of 0.005; but this still suggests that only one in two hundred infections was reported to their GP and correctly identified as influenza

The only notable quantitative differences when fitting to the two shortened time frames (compared to the distributions inferred when fitting to the complete time period) were elevated transmissibility levels (β), counteracted by an enlarged effect of prior infection (a) and vaccination propagation (ξ); further details are given in Section 4.2 of the S1 Text.

Considering type A influenza, Hill et al. (2019) clearly captured the alternating pattern of dominance by A(H3N2) and A(H1N1)pdm09 subtypes for the years 2012/13 to 2016/17; but more importantly the model was able to predict the unexpected result that A(H3N2) dominated in both 2016/17 and again in 2017/18. For influenza B, we obtained modest agreement for the overall magnitude of GP consultations as a result of type B, but this was not always in complete agreement with the subtype composition (Fig 5(a)).