key: cord-0303535-rhicsb95
authors: Haw, D. J.; Biggerstaff, M.; Prasad, P.; Walker, J.; Grenfell, B.; Arinaminpathy, N.
title: Using real-time data to guide decision-making during an influenza pandemic: a modelling analysis
date: 2021-06-12
journal: nan
DOI: 10.1101/2021.06.09.21258618
sha: 52936dc369fea8c5d30d0533b1c7642aee6b3cef
doc_id: 303535
cord_uid: rhicsb95

Influenza pandemics typically occur in multiple waves of infection, often associated with initial emergence of a novel virus, followed (in temperate regions) by a later resurgence accompanying the onset of the annual influenza season. Here, we examined whether data collected from an initial pandemic wave could be informative, for the need to implement non-pharmaceutical measures in any resurgent wave. Drawing from the 2009 H1N1 pandemic in 10 states in the USA, we calibrated simple mathematical models of influenza transmission dynamics to data for virologically confirmed hospitalisations during the initial spring wave. We then projected pandemic outcomes (cumulative hospitalisations) during the fall wave, and compared these projections with data. Model results show reasonable agreement for all states that reported a substantial number of cases in the spring wave. Using this model we propose a probabilistic decision framework that can be used to determine the need for pre-emptive measures such as postponing school openings, in advance of a fall wave. This work illustrates how model-based evidence synthesis, in real-time during an early pandemic wave, could be used to inform timely decisions for pandemic response.

illustrates the difference in size between the two waves. Notably, the geographically southern states of Georgia, 58 New Mexico and Tennessee reported only sparse data in the spring/summer period: these same states also 59 showed substantially fewer cases being reported in the fall wave per capita, when compared to other states. 60 To model these data, we calibrated a deterministic, compartmental model of influenza transmission dynamics, 61 with five age groups: <4 years old (yo), 5-19yo, 20-49yo, 50-64yo, and >65yo (see Materials and Methods). 62 We calibrated this model to data from the spring wave illustrated in Figure 1 , i.e. from months April-August. 63 For each location we then used the calibrated model to project the fall wave dynamics. Figure 2 shows results 64 in the example of California, illustrating both spring wave calibration, and fall wave projections. Figure For those states showing reasonable model performance, we next examined how this framework could be 77 operationalised, to trigger pre-emptive interventions in advance of the fall wave. Such interventions could 78 involve, for example, physical distancing orders; pre-emptive school closures; or other non-pharmaceutical 79 measures aimed at reducing opportunities for transmission. As such measures are typically costly and 80 disruptive, any decision to implement them must carefully balance these disruptions against the risks of 81 widespread morbidity and mortality.

As an illustrative example in the current analysis, we concentrated on pre-emptive school closures (i.e. 83 postponing the start of the school term), until a vaccine becomes available. To inform our assumptions for 84 vaccine roll-out, we assumed the same trajectory as in the H1N1 pandemic, when a vaccination programme 85 was in October, ultimately to cover over 25% of the population (see Figure S4 ). In a hypothetical scenario As a decision tool for when to trigger such measures, we defined the 'probabilistic risk score' (PRS) as the 91 probability that cumulative hospitalisations in the fall wave will exceed a threshold of h per capita. We 92 assumed that this risk score would be evaluated at the end of the spring wave, and that pre-emptive school In any future influenza pandemic, early and accurate information will be critical in deciding how best to 105 respond. Here we have examined how mathematical modelling of transmission dynamics could be used to 106 analyse surveillance data in the early stages of a pandemic, to inform decisions for pre-emptive sufficient data, this approach shows reasonable projections for cumulative fall wave burden (Fig.3) . A key 110 benefit of such a modelling approach is that it can be readily deployed in real time: we illustrate how this 111 model could be applied in a probabilistic way, to inform decisions for pre-emptive school closures (Fig.4) .

Model calibration to an unmitigated phase allows us to capture important epidemiological properties of an 113 3 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2021. ; https://doi.org/10.1101/2021.06.09.21258618 doi: medRxiv preprint outbreak, most crucially the basic reproductive number. Though such calibration does not require an entire wave to be unmitigated, any changes in contact patterns during the calibration period is likely to bring 115 additional uncertainty into the model.

Our modelling approach performs less well in states having only sparse data for the spring wave (Figures 1 117 and 3). Such sparseness could be explained either by under-reporting, or by a genuinely lower level of 118 influenza activity in these locations. However, it is notable that these states also reported systematically low 119 numbers in the fall wave as well (Figures 3 and S2) , suggesting that data reporting may be the driving factor. 120 We focused on data for virologically confirmed hospitalisation because it was the least affected by changes in 121 testing practices, during the pandemic [18] . Nonetheless, an important area for future work is to explore the 122 potential for incorporating other forms of data as well, including syndromic and virological surveillance 123 collected from the primary care level and above [14] . Combining different streams of data in this way could 124 offer a helpful approach, to compensate for shortfalls in any individual data stream.

As an example of non-pharmaceutical interventions, we have modelled pre-emptive school closures, i.e. 126 postponing the opening of schools. We note that our estimates for the impact of these measures are driven by 127 modelled variations in the age-specific contact matrix, depending on whether schools are in or out of session.

In turn, these variations are derived from estimated contact rates in an education setting[2]. In future, such 129 estimates would benefit from primary evidence for the 'real world' impact that could arise from pre-emptive As with any modelling study, our analysis has limitations to note. Our mathematical model involves several 139 simplifications: averaging at the state level, it does not address the marked intra-state, spatial heterogeneity 140 seen in the 2009 pandemic [8], indeed heterogeneity that is likely to be displayed by any future pandemic as 141 well. Further work could seek to address these complexities by incorporating spatial structure. However, it 142 would be important for any such approach to maintain a balance between complexity, and rapid deployability, 143 during a pandemic. As noted above, our work illustrates that even a simple model is able to capture the 144 cumulative fall wave burden in reasonable agreement with the data. Nonetheless, more complex models may 145 be helpful in better capturing the peak timing of the fall wave: an estimate that could be equally important intervention.

The Model 165 We use a deterministic SIR (susceptible-infectious-removed) model of influenza transmission defined as follows:

where S V denotes vaccinated susceptibles, S V P vaccinated susceptibles with active vaccine protection, I S 167 symptomatic infectious, I A asymptomatic infectious, and the subscript i indexes 5 age groups (0-4, 5-19, as a multiplicative factor of symptomatic incidence, using the case-hospitalisation ratios given in [18] .

Vaccination rates and hospitalisation multipliers are given at national level only.

Uncertainty in disease incidence is captured via uncertainty in case-hospitalisation multipliers. These are 177 assumed normally distributed for each age group i, with mean µ i and standard deviation σ i , given in table 1.

For parameter set θ, our model produces simulated weekly incidence y(t), desegregate by age group. These 179 5 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2021. ; Figure 1 : FluSurv-NET data from the 2009 H1N1 pandemic in the USA. Shown is weekly, agespecific data collected by the US Centers for Disease Control and Prevention (CDC), for hospitalisations that were virologically confirmed as being pandemic H1N1. Each colour denotes a different age group, as indicated by the legend. Panels show data from the different states reporting FluSurv-NET data. Weeks are numbers along the x-axis according to MMWR numbering with, for example, week 35 corresponding to the week beginning on Sunday 30th August. Note that the y-axis varies between states. As described in the main text, several of these states (e.g. California) show clear signs of distinct spring and fall waves. For the purpose of the model, we used these data in combination with CDC estimates for the proportion of symptomatic cases that are hospitalised, virologically tested, and reported through this dataset. 6

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The copyright holder for this preprint this version posted June 12, 2021. ; Figure 2 : Illustration of the modelling approach, and of model projections, in the example of California. For each state shown in Fig.1 , we calibrated the model to the epidemic data from the spring wave (black line, to the left of the vertical dashed line, with aggregated model projections shown in grey shaded area). Using this calibrated model, we projected simulations forward into the fall, taking account of the effect of school openings and environmental forcing (blue shaded area). Although the model projection for epidemic peak timing varied in accuracy across states, our subsequent analysis concentrates on cumulative burden (area under the curve). See Figure S1 for results for other states.

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The copyright holder for this preprint this version posted June 12, 2021. ; 8 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted June 12, 2021. ; Figure 5 : Proposed decision framework for triggering pre-emptive non-pharmaceutical interventions (NPIs), in advance of the fall wave. Shown, for illustration, is the example of California. These plots can be interpreted as cumulative probability distributions, for the total hospitalisations projected in the fall wave. As described in the main text, we define a 'probabilistic risk score' (PRS) as the probability that fall wave hospitalisations will increase a given threshold, h. We assume that pre-emptive interventions would be triggered if PRS exceeds some threshold probability P , with both H and P determined by a policymaker. The figure shows an illustrative scenario where h = 1, 500 cumulative hospitalisations, and P = 0.1 ('reference point', shown as a black dot). Any model-based projections can be represented as a downward-sloping curve on this plot: pre-emptive interventions would be triggered if the curve intersects the vertical, dashed line at any point above the reference point. As examples, the blue curve shows model projections for a 2009-pandemic-like virus in California (i.e. corresponding to Fig.3A) , a scenario that would not trigger pre-emptive interventions. The solid red curve shows an alternative scenario, of a virus that is equally infectious, but twice as severe (i.e. having twice the risk of hospitalisation given infection). Such a virus would trigger preemptive interventions; the dashed red curve shows the reduction in hospitalisation risk that would occur, in a scenario where school opening is postponed for 10 weeks until vaccine rollout is underway (assuming the same vaccine introduction and rollout scenario as occurred in 2009-2010, in response to the pandemic).

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The copyright holder for this preprint this version posted June 12, 2021. 13 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)

The copyright holder for this preprint this version posted June 12, 2021. ; https://doi.org/10.1101/2021.06.09.21258618 doi: medRxiv preprint Figure S1 : Cumulative hospitalisations by state in the first (left) and second (right) waves of the 2009 influenza pandemic. The second wave is counted from week 35(inclusive), the week of 1st September.

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The copyright holder for this preprint this version posted June 12, 2021. ; https://doi.org/10.1101/2021.06.09.21258618 doi: medRxiv preprint Figure S2 : Model calibrations and projections by state.

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The copyright holder for this preprint this version posted June 12, 2021. ; https://doi.org/10.1101/2021.06.09.21258618 doi: medRxiv preprint Figure S3 : Marginal densities of the Bayesian fit to first-wave data for California: basic reproductive number R 0 and recovery rate γ (top); R 0 and amplitude of seasonality φ 2 (bottom). 

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