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Correspondence to: Jodie McVernon, Murdoch Childrens Research Institute & Melbourne School of Population Health, The University of Melbourne, Parkville Victoria 3010. Fax: (03) 9348 1827; e-mail: email@example.com
Objective: To define optimum use of the national antiviral stockpile during the early phases of the response to pandemic influenza in Australia, to inform the 2008 revision of the Australian Health Management Plan for Pandemic Influenza.
Methods: A mathematical model was used to compare strategic uses of antiviral agents for treatment and post-exposure prophylaxis to limit transmission until availability of a strain-specific vaccine. The impact of provision of pre-exposure prophylaxis to healthcare workers (HCWs) on the ability to control the epidemic was also assessed.
Results: Optimal constraint of epidemic growth was achieved by intensive ascertainment of contacts of cases for post-exposure prophylaxis for as long as feasible. While pre-exposure prophylaxis of healthcare workers utilised a substantial proportion of the stockpile, this did not impede disease control or the ability to treat cases. Absolute delays to outbreak depended on both the intervention strategy and the growth rate of the epidemic. As vaccination was only effective when introduced before explosive growth, this timing was critical to success.
Conclusions and implications: Liberal distribution of antiviral drugs to limit disease spread for as long as is feasible represents optimal use of these agents to constrain epidemic growth. In reality, additional non-pharmaceutical control measures are likely to be required to control transmission until vaccines can definitively contain pandemic influenza outbreaks.
Recent concerns regarding emergence of a pandemic influenza strain have prompted the development or revision of preparedness plans by governments and public health agencies. The Australian Government Department of Health and Ageing (DoHA) revised the Australian Health Management Plan for Pandemic Influenza (AHMPPI) in 2008.1 This revised plan builds on the key concepts outlined in the AHMPPI 2006, but takes into account the experience of Exercise Cumpston 2006, a national pandemic planning exercise, as well as the expanded national stockpile of antivirals and improvements in vaccine technology.
A critical shift in thinking in the AHMPPI 2008 is inclusion of a new SUSTAIN phase, inserted between the initial CONTAIN phase and the CONTROL phase, when mass vaccination will be used to provide definitive control of the pandemic in Australia (Table 1). A key objective for SUSTAIN is identification of interventions to limit transmission that may be feasibly delivered over an extended period of time, until a sufficient proportion of the population has been immunised with a strain-specific vaccine to control the pandemic.
Table 1. Key actions by pandemic phase, Australian Health Management Plan for Pandemic Influenza, 2008.
A novel virus with pandemic potential causes severe disease in humans who have had contact with infected animals. There is no effective transmission between humans. Novel virus has not arrived in Australia.
1. Alert: increased vigilance for cases. Remaining alert to the risk of a pandemic and increased monitoring of the virus (to look for genetic mutations in the virus).
2. Support the overseas response to control the source. Working with the agriculture and health sectors in overseas affected countries to reduce the amount of the pandemic potential virus circulating in animals and to protect humans from infection.
1. Delay entry of the virus to Australia using border measures.
OS4: Small cluster of cases in one country overseas.
2. Support the overseas response to control the source. Try to avert a pandemic by rapid intervention in the affected areas.
OS5: Large cluster(s) of cases in only one or two countries overseas.
3. Enhanced vigilance – increased vigilance for cases (overseas and domestically) and increased monitoring of the virus (to look for genetic mutations in the virus).
OS6: Large cluster(s) of cases in more than two countries overseas.
4. Escalate preparedness activites for possible pandemic (that is, get ready to implement).
5. Stand-down the response if the pandemic is averted before it arrives in Australia.
CONTAIN AUS 6a
Pandemic virus has arrived in Australia causing small number of cases and/or small number of clusters.
1. Contain the establishment of the pandemic strain in Australia.
2. Ensure the health system is best able to cope with an influenza pandemic.
SUSTAIN AUS 6b
Pandemic virus is established in Australia and spreading in the community.
1. Sustain the response while we wait for a customised pandemic vaccine to become available.
2. Minimise transmission and maintain health services.
CONTROL AUS 6c
Customised pandemic vaccine widely available and is beginning to bring the pandemic under control.
1. Control the pandemic with vaccine.
2. Careful downscaling of response as the pandemic is brought under control, to an eventual standing down of control measures in recover.
RECOVER AUS 6d
Pandemic controlled in Australia but further waves may occur if the virus drifts and/or is re-imported into Australia.
1. Recover and restore the health system and return to ALERT phase as quickly as possible.
2. Enhanced vigilance for a subsequent wave. Increased vigilance for cases and increased monitoring of the virus (to look for mutations).
Mathematical models of infection, while necessarily simplifications of complex biological and sociological systems, allow systematic exploration of a range of alternative outbreak and intervention scenarios. Here we report on the modelling work provided to the Office of Health Protection (OHP), DoHA, that aimed to define optimal deployment and duration of antiviral drug interventions during the CONTAIN and SUSTAIN phases.
Mathematical model of influenza transmission
The susceptible-exposed-infectious-recovered (SEIR) model of influenza transmission has been described previously2 and in the supplementary material. At the beginning of the outbreak, the entire population is assumed susceptible (S) to the pandemic strain. Individuals who contract infection pass briefly through a latent phase (E) before becoming infectious. Infectious individuals may be symptomatic (I) or not (A). All infected individuals are assumed resistant (R) to reinfection upon recovery.
A novel feature of the model is incorporation of a dynamic ‘contact’ label, applied to a fixed number of individuals drawn from the whole population each time a new infectious case (I or A) appears. We define these contacts, based on sociological studies,3 as those people who have been sufficiently close to an infected individual to conceivably contract infection and so may be considered eligible for post-exposure prophylaxis. Infections can only occur in individuals who have been in contact with a case. The uninfected contacts, comprising the majority, return to their original ‘non-contact’ status within a matter of days.
The primary difference between CONTAIN and SUSTAIN is the level of effort applied to contact tracing. Given the likelihood that spontaneous social distancing will take place as the outbreak unfolds, we define the total number of contacts (κ) during CONTAIN as 30, and 20 during SUSTAIN. The breakdown of household and community contacts by location, is shown in Table 2, with the SUSTAIN estimates based on proportionate numbers of encounters reported from different social settings.4 Figures are deliberately inflated during CONTAIN to account for the more exhaustive contact tracing efforts anticipated during this phase, including provision of post-exposure prophylaxis to individuals exposed in healthcare settings, with implications for stockpile depletion. The number reported as ‘traced’ in the table during each phase reflects the relative effort employed, with household level contacts considered the most readily identifiable, followed by work/social/school acquaintances.
Table 2. Model assumptions regarding contact numbers in CONTAIN & SUSTAIN (loosely based on Edmunds et al4).
Work / social / school
Other community contacts
Assumptions regarding infection transmission
We do not explicitly characterise symptom onset in our model, but assume a one-day latent period between inoculation and the onset of 1.5 days' infectiousness, of which at least part of one day is likely presymptomatic. Within our deterministic model framework, this corresponds to a serial interval of 2.5 days.5
As in the AHMPPI 2008,1 we consider an unmitigated overall pandemic attack rate in the order of 60%. One third of infections are assumed asymptomatic (α≅ 0.3), giving an unmitigated clinical attack rate of around 40%. Asymptomatic cases cannot be identified and treated, nor can their contacts be offered prophylaxis. We consider such individuals to be as contagious as those with symptoms, to explore the ‘worst case’ implications of subclinical infection spread. This assumption is plausible, given observations of ‘off-season’ influenza transmission in households, without illness.6
Assumptions regarding antivirals
Distribution of antivirals for treatment and prophylaxis may be modelled within this framework (Figure 1). Prophylaxis divides the contact class in two: the proportion (ɛ) of contacts of symptomatic cases (α) that receives antiviral agents (Cp) and the remainder (1-αɛ) that does not (Cnp). Prophylaxis reduces susceptibility to infection by a factor (es).7 Protection is incomplete, however, and some of those provided with preventive therapy develop breakthrough infections, deemed less infectious (ei) than untreated cases.8 Contacts who have not been given prophylaxis are fully susceptible to infection. A proportion (ψ) of these will be identified within 48 hours of symptom onset and treated, with a resultant reduction in infectiousness (et).9
We have assumed a 50% reduction in susceptibility for contacts receiving antivirals.7 Our estimates for the reduction in infectiousness attributable to drug treatment are conservative, at only 20%. Parameter assignments are summarised in Table 3.
Table 3. Parameter assignments used in the model.
Number of contacts traced
Duration of contact phase (1/δ)
Latent period (1/ω)
Infectious period (1/γ)
Final serologic attack rate
Asymptomatic proportion (1-α)
Relative infectiousness of asymptomatic cases (χ)
Antiviral Intervention Parameters
Total number of courses of antivirals in the stockpile
0.4 × population size
Proportion of symptomatic cases identified and treated (ψ)
Proportion of contacts receiving prophylaxis (ɛ)
Relative susceptibility on prophylaxis (es)
Relative infectiousness of breakthrough on prophylaxis (ei)
Relative infectiousness of treated cases (et)
Initiation of interventions within our model corresponds to Phase CONTAIN 6a (Table 1),1 during which novel virus has arrived in Australia causing small numbers of cases and/or small numbers of clusters. We assume a detection threshold of 10 new incident cases reported nationally on a given day before the CONTAIN intervention is commenced, switching to SUSTAIN later in the simulation.
The diminishing size of the antiviral stockpile is tracked by accounting for all courses of antiviral drugs distributed as treatment or prophylaxis, allowing prediction of the lifetime of the stockpile under various usage scenarios.
Assumptions regarding vaccination
As the stated objective of antiviral use is to ‘buy time’ for distribution of a strain-specific vaccine, we further modelled a mass immunisation program. Vaccine responses were assumed protective one week following a two-dose immunisation schedule, administered 21 days apart. Vaccine roll-out to the whole population was projected over one year.
In the absence of specific data to inform the likely efficacy of a pandemic vaccine, complete protection of 70% of vaccinees was assumed, with no protection among the remainder. Recognising that a proportion of immunised individuals may have already become resistant following infection, the model only reports effective immunisation of 70% of the susceptibles vaccinated. We consider the interaction between the rate of epidemic growth and timing of vaccine introduction for success of containment.
Delays to outbreak achieved using different antiviral distribution strategies
As Figure 2 demonstrates, use of antivirals alone was only able to ‘buy time’ until an inevitable epidemic. We, therefore, compared delays to outbreak achievable for a range of strategic drug uses. Consistent with earlier findings,2 a strategy focused solely on case treatment had little impact (Table S2, supplementary material). However, provision of prophylaxis to contacts was able to constrain epidemic growth, with more intensive CONTAIN measures (Figure 2b) demonstrably more effective than SUSTAIN (Figure 2a). Implementation of the CONTAIN strategy was considered feasible up to a total of 1,000 new incident cases per day nationwide (Figure 2b, 2c). However, this high-intensity strategy was consistently superior, even if only employed for a matter of weeks or up to a threshold of 100 new incident cases per day (Table S2, supplementary material). At cessation of CONTAIN, implementing a SUSTAIN program alongside treatment until stockpile depletion (Figure 2c) was beneficial compared with continuing treatment alone.
The importance of stockpile size was explored by modelling distribution of antivirals for continuous pre-exposure prophylaxis to 300,000 dedicated healthcare workers (HCWs) over an 18-week period, until vaccine availability. Although this consumed 3.68 million drug courses, little effect on the population experience of disease was observed. As previously demonstrated, drug delivery mirrors epidemic growth, which is exponential.2 Thus, in the absence of logistic constraints, a substantial proportion of the stockpile will be distributed within the days immediately before depletion (Figure 3).
Reduction in final attack rate with use of strain-specific vaccine
When considering the impact of immunisation superimposed on antiviral use, it was apparent that timing of vaccine introduction relative to growth of the mitigated epidemic was critical. To demonstrate this point, we report a single, credible timepoint for vaccine introduction of 14 weeks (i.e. first effective protection observed by 18 weeks) and vary the growth rate of the underlying epidemic. Figure 4 shows the cumulative number of individuals who become resistant either through natural infection or vaccination for the same control measures imposed on epidemics with a baseline attack rate (AR) of 37%, 40% or 43%. The corresponding baseline reproductive numbers (R0), or number of secondary cases arising from each index case at the start of the epidemic, are 1.42, 1.48 and 1.55. As can be seen, a very small increase in AR from 40 to 43% is associated with a markedly worse outcome for the population.
The other key model assumption that controls epidemic growth is the serial interval, or time from the onset of a primary case to a secondary case. Our model conservatively assumes a very short interval of 2.5 days. Recent models of influenza use estimates ranging from 2.6 days10 to 3.5 days.11 For the 43% AR scenario with interventions (Figure 4c), increasing the serial interval to three days reduced the final mitigated attack rate from 29% to only 6%. For a serial interval of 3.5 days, a mitigated attack rate of 0.4% was achieved (Table S3, supplementary material).
Relative usage of antiviral drugs for strategic indications
Figure 3 demonstrates the exponential increase in drug distribution required to keep up with epidemic growth and hence ‘production’ of new contacts in the model, which may or may not be sustainable.
The model reports the number of drug courses used for different indications. For the above case, with 18 weeks' continuous HCW pre-exposure prophylaxis, 46% of the stockpile is consumed by HCWs alone. Seven per cent is distributed during CONTAIN, of which 96% is used for prophylaxis (4% for treatment). SUSTAIN consumes the final 47% of doses, with 86% distributed for prophylaxis.
Further exploration of the model's sensitivity to key parameter assignments related both to the baseline epidemic and the effectiveness of proposed interventions is detailed in Section S3 of the supplementary material. In brief, assumptions associated with a higher baseline transmission rate, including higher clinical attack rate, greater asymptomatic proportion and shorter serial interval made the epidemic more difficult to control. Similarly, lower achievable antiviral coverage and/or efficacy reduced the ability of the intervention to delay the outbreak. Intuitively, time to initiation of the vaccination program and the speed of its rollout to achieve ‘protective’ threshold coverage were additional critical determinants of the final clinical AR.
Application of a CONTAIN strategy, with intensive contact tracing, was more effective at limiting transmission of infection than prophylaxis of household contacts alone. The most effective intervention deemed feasible was continuation of CONTAIN until an incident case number of 1,000 per day nationwide, followed by a switch to SUSTAIN. Failure to provide ongoing prophylaxis to household contacts during SUSTAIN led to poorer outcomes. Concurrent treatment of cases throughout had synergistic benefits for outbreak control and consumed less than 10% of the stockpile.
Provision of continuous pre-exposure prophylaxis to 300,000 HCWs consumed 46% of the stockpile over 18 weeks. While appreciably depleting resources, such use had a negligible impact on the containment effort. This is because drug distribution follows the exponentially growing epidemic, meaning that the last half of the stockpile was consumed in a matter of days. Conversely, doubling the stockpile would buy little more than a week's additional delay to outbreak for the scenarios reported.
Mass immunisation with an assumed vaccine efficacy of 70% was able to control the outbreak within a matter of weeks. This was due to the relatively low critical immunisation coverage (29%) required to impede transmission of a pathogen with an R0 of 1.4.12 The relative modesty of this target may be helpful for policy makers considering strategic distribution of limited resources. The key determinant of vaccine impact on the final attack rate, however, was the phase of the epidemic at which vaccination was introduced. For many of the scenarios explored, antiviral stockpile depletion before vaccine availability had already allowed the definitive outbreak to occur. If the outbreak had been successfully delayed, dramatic AR reductions were possible.
We have opted for a simple, analytically tractable model structure in which to investigate infection spread under a range of interventions. This has, however, been at the cost of ‘real world’ complexity. Our use of a deterministic model has limitations. The inherently stochastic nature of the epidemic in its early stages cannot be accounted for accurately, including the possibility of both epidemic die-out and ‘super-spreading’ events.13 The dynamics of the established epidemic, however, should be reasonably well captured. Further, we employ the simplest homogeneous mixing assumption, with no attempt made to represent the distinct behaviours or characteristics of population subgroups that may critically influence infection spread.14 While recognising the limitations of this approach, it is worth noting that homogeneous-mixing compartmental models have proved to be both robust and predictive in many instances.15
The population is considered fully susceptible at the beginning of the outbreak. On this basis, a clinical attack rate of 40% and an asymptomatic attack rate of 20% correspond to an R0 of around 1.4. If 40% of the population is actually immune at baseline, the same clinical attack rate will be observed for an organism with a true R0 of 3.2. Variable levels of prior immunity in distinct host populations may result in markedly different clinical attack rates for an organism with a given R0. Accordingly, control of an imported infection may be more or less difficult than supposed from observation of the source outbreak.16 Further, individuals who have recovered from infection are assumed fully resistant to reinfection in the model. Historical reports of secondary cases of influenza occurring within weeks or months of an initial illness cast doubt on this assumption.17 Were individuals even partially susceptible following the infectious period, outbreak control could prove more challenging,16 with the possibility of recurrent epidemic waves.
Full sensitivity of circulating influenza strains to the antiviral agent(s) in use is assumed. Depending on the rate of seeding and relative transmissibility of drug-resistant strains, containment efforts could be hindered or seemingly paradoxically aided by resistance emergence.18,19 Reduced transmissibility of neuraminidase-inhibitor resistant influenza strains, while sometimes observed,20 cannot be assumed in a pandemic scenario. The H274Y mutation, identified in 14% of 437 European H1N1 influenza strains (70% of Norwegian strains) between November 2007 and January 2008, is associated with a 400-fold reduction in susceptibility to oseltamivir. None of these mutant isolates have been taken from treated individuals, making it likely that they are readily transmissible between humans.21
Our findings strongly support application of an intensive contact tracing effort for post-exposure prophylaxis in the early stages of pandemic influenza for as long as feasibly possible. Continuous distribution of antiviral prophylaxis to healthcare workers (HCWs) is considered necessary in the early phases of the pandemic response to ensure continuity of healthcare services and does not compromise population disease control or the capacity to treat critically ill patients. Conversely, provision of treatment to cases if clinically indicated is likely to have a synergistic impact on disease control and does not compromise the availability of antivirals for use in post-exposure prophylaxis. Optimal benefit of a strain-specific vaccination program depends on the combined effectiveness of pharmaceutical and non-pharmaceutical interventions to constrain epidemic growth until its implementation. How difficult this task will be to achieve in practice is contingent upon the transmissibility of an emergent pandemic strain and the level of existing immunity in the population, both of which will remain unknown until the event. Early characterisation of epidemic growth rates5 and ongoing monitoring for antiviral efficacy and emergence of drug resistance will be critical in a pandemic scenario to guide further decision making.
We are indebted to Niels Becker (National Centre for Epidemiology and Population Health, Australian National University), John Mathews, Chris McCaw, Paul Pallaghy (Melbourne School of Population Health, The University of Melbourne) and James Wood (School of Public Health & Community Medicine, University of New South Wales) for many helpful discussions and comments during development of the modelling approaches that underpin this work. Model scenarios were identified and refined in extensive consultation with Julie Hall, then Principal Medical advisor to the Office of Health Protection, who also provided helpful feedback during the reporting phase. We were also grateful for input from members of the Chief Medical Officer's Scientific Influenza Advisory Group.
This work was funded by the Office of Health Protection, Australian Government Department of Health and Ageing (DoHA). Support for the model's development phases was provided by DoHA and the National Health and Medical Research Council (NHMRC) through Capacity Building (ID 358425), Urgent Research (ID 410224) and Training Fellowship (ID 359238) schemes.
Figure 1: Simple schematic of the intervention model.
In the steady state, a proportion (ɛ) of contacts of symptomatic (α) cases who are susceptible will be administered antiviral prophylaxis, thereby reducing their susceptibility by a factor es. Of those who do not receive prophylaxis and go on to develop symptomatic (α) infection, a proportion (ψ) will be identified and treated. The infectious potential of treated cases and breakthroughs on prophylaxis is reduced by factors et and ei, respectively.
Figure 2: Impact of antiviral interventions on outbreak timing.
Epidemic prevalence curves at baseline (solid line) and with interventions (dashed line). Depletion of the antiviral stockpile is shown by the dotted line. Four distinct antiviral distribution strategies are modelled: a) Case treatment is combined with targeted prophylaxis of close contacts only (SUSTAIN stratgy), achieving some delay to outbreak. b) Case treatment is combined with intensive contact tracing until a threshold of 1,000 new incident cases per day is reached. Greater delays are achieved and the stockpile is not consumed. c) As for b), but with a switch to the SUSTAIN strategy at 1,000 new incident cases per day. The outbreak is controlled for a few more weeks with complete utilisation of the residual stockpile for close contact prophylaxis. d) As for c), but with continuous provision of antiviral prophylaxis to 300,000 healthcare workers (HCWs) for 18 weeks. The epidemic remains well-controlled at a population level within the constraints of the depleted stockpile.
Figure 3: Time course of drug distribution relative to epidemic growth phase.
Drug distribution is modelled for a scenario with a baseline clinical AR of 40%, upon which is imposed antiviral treatment combined with intensive contact tracing (CONTAIN) until 1,000 new incident cases. Above this threshold, there is a shift to close contact provision of prophylaxis only (SUSTAIN) until the stockpile expires. a) Prevalence curve for the mitigated epidemic. b) Number of drug doses distributed per day for treatment (lower line) or prophylaxis (upper line). Note the log scale y-axis.
Figure 4: Impact of vaccination on final clinical attack rate, for different epidemic scenarios.
Cumulative prevalence curves for case numbers at baseline (solid line) and with interventions (dashed line). The intervention scenario modelled is as in Figure 2d) comprising case treatment, continuous HCW prophylaxis for 18 weeks and targeted intensive (CONTAIN) prophylaxis until 1,000 new incident cases per day followed by a switch to close contact prophylaxis only (SUSTAIN). Antiviral stockpile depletion is shown by the dotted line. The dash-dotted line denotes the cumulative number of susceptibles who are protected by vaccination from 18 weeks following initiation of control measures, rolled out over the course of several months. The impact of interventions is considered in relation to the baseline (unmitigated) clinical attack rate (AR). a) AR 37%– successful containment is achieved, with a final mitigated AR of 0.02% (i.e. no visible dashed line). b) AR 40%– again, the epidemic is contained, with a final mitigated AR of 0.17%. c) AR 43%– antivirals are not able to constrain epidemic growth until vaccines are available, leading to only partial mitigation and a final AR of 29%.