Reducing disease burden in an influenza pandemic by targeted delivery of neuraminidase inhibitors: mathematical models in the Australian context

Background Many nations maintain stockpiles of neuraminidase inhibitor (NAI) antiviral agents for use in influenza pandemics to reduce transmission and mitigate the course of clinical infection. Pandemic preparedness plans include the use of these stockpiles to deliver proportionate responses, informed by emerging evidence of clinical impact. Recent uncertainty about the effectiveness of NAIs has prompted these nations to reconsider the role of NAIs in pandemic response, with implications for pandemic planning and for NAI stockpile size. Methods We combined a dynamic model of influenza epidemiology with a model of the clinical care pathways in the Australian health care system to identify effective NAI strategies for reducing morbidity and mortality in pandemic events, and the stockpile requirements for these strategies. The models were informed by a 2015 assessment of NAI effectiveness against susceptibility, pathogenicity, and transmission of influenza. Results Liberal distribution of NAIs for early treatment in outpatient settings yielded the greatest benefits in all of the considered scenarios. Restriction of community-based treatment to risk groups was effective in those groups, but failed to prevent the large proportion of cases arising from lower risk individuals who comprise the majority of the population. Conclusions These targeted strategies are only effective if they can be deployed within the constraints of existing health care infrastructure. This finding highlights the critical importance of identifying optimal models of care delivery for effective emergency health care response. Electronic supplementary material The online version of this article (doi:10.1186/s12879-016-1866-7) contains supplementary material, which is available to authorized users.

7.5% (4.9%, 11.1%) 7.7% 6.8% (4.4%, 9.7%) 6.9% High Tx/ Mod 2 7.5% (4.9%, 11.1%) 7.7% 6.8% (4.4%, 9.7%) 6.9% High Tx/ Mod 3 7.6% (4.9%, 11.2%) 7.8% 6.8% (4.5%, 9.8%) 7.0% High Tx/ Mod 4 7.7% (5.0%, 11.3%) 7.8% 6.9% (4.5%, 9.9%) 7.0% High Tx/ Sev   Table S3: Stockpile usage is reported in terms of the total number of packets that were distributed for treatment of community and hospital presentations and for post-exposure prophylaxis ("Net Usage") and also by the number of packets that were used to treat hospitalised cases ("Hospital Rx"). Key message: Liberal antiviral use in the community ("Rx All/PEP Eld, HR" and "Rx All" strategies) increases the net stockpile consumption but can decrease hospital consumption in the high-severity scenarios. Prophylaxis makes a substantial additional drain on the stockpile.  Table S4: Outpatient stockpile usage is reported in terms of the number of treatment packets that were distributed to persons infected with pandemic influenza ("Outpatient Flu") and to persons not infected with pandemic influenza but presenting with ILI ("Outpatient Non-Flu"), who may receive treatment when a syndromic indication is considered sufficient for initiation of treatment. Key message: When using syndromic indication to initiate treatment in the community, the number of doses provided to patients that are not infected with pandemic influenza is less than the number used for effective treatment in the community.  Table S5: Initial Action Phase stockpile usage is reported in terms of the number of packets that were distributed for treatment ("Treatment") and in total ("Net"). Key message: Stockpile consumption in the Initial Action Phase is very low in all pandemic scenarios, compared to the net consumption over the course of the entire epidemic (previous tables), even when the number of prophylaxis courses greatly exceeds the number of treatment courses.    In all scenarios, liberal antiviral use in the community ("Rx All/PEP Eld, HR", "Rx All" and "Rx At-Risk, Hosp" strategies) can prevent more deaths than is achieved by providing treatment solely to hospitalised cases ("Rx Hosp" strategy).

Strategy Presentation Hospitalisation
Low  Table S9: The relative risks of presenting (at either an outpatient or inpatient setting) and of requiring hospitalisation (regardless of actual bed capacity) are shown below. These relative risks are calculated with respect to identical pandemic scenarios in the absence of antiviral interventions for both the Initial Action and Targeted Action phases. Key message: Antiviral interventions produce minor reductions in the relative risk of presentation (except when the intervention can mitigate the epidemic), but can significantly reduce the relative risk of hospitalisation in even the most severe scenarios through the provision of early treatment (in the community) to cases that would otherwise require hospitalisation.  Table S10: The relative risks of requiring ICU admission (regardless of actual ICU capacity) and death are shown below. These relative risks are calculated with respect to identical pandemic scenarios in the absence of antiviral interventions for both the Initial Action and Targeted Action phases. Key message:

Scenario
The relative risks of ICU admission and deaths are substantially reduced when treatment is only provided to hospitalized cases ("Rx Hosp" strategy). Additional provision of treatment to community presentations reduce these risks even further -compare the relative risks in the worst case scenario (high-transmission high-severity) for the liberal strategies ("Rx All/PEP Eld HR" and "Rx All") to the "Rx Hosp" strategy.

S2 Model equations
The transmission model used in this paper involves one major modification to the contact model first introduced in [1] and further developed in [2,3]. In this study, the population was stratified into five distinct risk groups (young children, elderly, high-risk, health care workers, and the general adult population), to allow for differential risks of severe outcomes, differential benefits conferred by antiviral treatment, and targeted treatment and prophylaxis strategies. We assumed these groups mixed homogeneously. The model structure is shown in Figure S1.  The proportion of all infected cases that present (α) is the sum of the severe cases (all of which present) and the proportion (α M ) of the remaining (i.e., mild) cases that present:

S
We have assumed that α M is dependent on the severity of the epidemic (η), as first defined in [3] and illustrated in Figure S2.
In recognition that not all contacts of an infectious individual can be identified and provided with post-exposure prophylaxis, the parameter σ defines the proportion of contacts that are potentially identifiable. Accordingly, the proportion of all contacts that receive prophylaxis (ϵ) cannot exceed σ.
Finally, the fraction of presenting cases that receive treatment (ψ) and the fraction of contacts that receive prophylaxis (ϵ) are functions of time, since they are both affected by the logistical constraints introduced in this model and do not remain constant throughout an epidemic.
The original SEIR model [2] introduced Θ p and Θ np , which define the proportion of susceptible contacts in the population: The force of infection (λ) arises from the five infectious classes just as in the original SEIR model [2], given the number of infections per unit time made by an infectious individual (β): We have previously extended this model to include vaccination [3], but for the purposes of this study we assumed that no vaccine would be available.

S3 Latin hypercube sampling
Note that the combination of α rel and the most conservative value of e s provides an upper bound matched to estimates of prevention of clinical symptoms and a lower bound consistent with greatest efficacy in household settings ( Table S11: Model parameter distributions used in all pandemic scenarios. Each parameter is associated with a beta distribution (top), a uniform distribution (second), a log-uniform distribution (third), or a single value (bottom).