We consider social distancing interventions for a number of reasons; to better understand the effect which individual social distancing measures have on the attack rate and consequential mortality rate; to determine their sensitivity to the time of activation; to address scenarios where supplies of antiviral drugs and suitable vaccines are in limited supply, either due to an outbreak occurring in a country with little access to these resources drugs, due to logistical delays in their distribution and administration or due to the unavailability of an appropriately "typed" vaccine, particularly at the early states of a pandemic.
Antiviral drugs and social distancing interventions share several common characteristics: neither confers long-lasting immunity, and both deplete limited resources once in operation (a drug stockpile on one hand, and public patience on the other). The use of antiviral drugs is a core feature of the pandemic preparedness plans of many countries, such as the United States, the United Kingdom, and Australia [4
]. Their use in an influenza pandemic is however an untested strategy: more experience is needed to determine their likely effectiveness and optimal use, especially given the possibility of the development of antiviral drug resistance during or prior to a pandemic [17
]. It therefore seems prudent to consider social distancing interventions as an alternative or complement to antiviral-based strategies.
Social distancing interventions are important as they represent the only type of intervention measure guaranteed to be available against a novel strain of influenza in the early phases of a pandemic. They may be readily activated and thought of as a first line of defence in developing and developed countries alike. For the purposes of our study we have assumed that once intervention measures have been activated they continued indefinitely. The final attack rates reported thus represent ideal scenarios: preliminary results of additional research indicate that interventions would need to continue for approximately 5 months to prevent an epidemic with an R0
of 2.5, which is clearly unrealistic. While long-term imposition of socially and economically disruptive measures is not possible, social distancing interventions may be used to buy time for the establishment of an antiviral containment programme and/or the distribution of a vaccine [4
The historical record indicates that social distancing measures may be implemented, relaxed and sometimes re-implemented [6
]. Other models have investigated the optimal timing for rescinding and re-implementing social distancing interventions [21
]. However our results show what may be expected of social distancing interventions when implemented early and maintained indefinitely (or in practical terms, until an effective vaccination programme has been completed); and we establish maximum activation delays allowable if such interventions are to fulfil their potential.
The results are applicable to industrialised populations and are possibly not applicable to developing countries having lower population mobility and/or higher population densities. In such countries we may find higher daily contact rates and hence reduced opportunities for limiting contact and in achieving isolation in the household by non-pharmaceutical means.
When comparing our results to those of other models, differences arise which may be due to alternative assumptions being made regarding the demographics and contact behaviour of the population, and to different assumptions regarding interventions and the methods for deploying them. However, we are able to comment at a general level on how our results relate to that of methodologically similar studies.
The work of Glass et al [5
] most closely resembles that of ourselves, whereby they utilise a population of 10,000 individuals and, like us, examine only non-pharmaceutical interventions. Their model represents the estimated structure and contact patterns of a synthetic town in the USA; it is unclear to us how the differences in the detail modelled, between an actual population (Albany, Australia in our case) and this synthetic town affect the quality of the results obtained. The results coincide well for an R0
of 1.5 to 1.6, when considering school closure as the only intervention. With an R0
of 2.5 and all non-pharmaceutical interventions activated together, the results in [5
] suggest a reduction in the illness attack rate in the range 10% to 20%, depending on variation of the contact patterns assumed. By contrast, the results presented here suggest that an attack rate of as low as 3% may result if all interventions are activated optimally, that is within the first week of the arrival of an outbreak-producing index case and held indefinitely. One difference which may explain this variance is that Glass et al assume a threshold of 10 diagnosed cases in a school before closure is effected compared with the optimal strategy adopted by ourselves. This again highlights the significance of rapid intervention if we are to prevent an epidemic, or to substantially reduce its rate of growth.
In comparing whole-country models such as that produced for the USA by Germann et al [13
], the only control interventions which can be directly compared is that of school closure in isolation. The simulated attack rate for unmitigated epidemics with R0
= 1.5/1.6 are reduced to 1% and 13%, comparing the Germann et al result with that presented here. What is perhaps more interesting is that for R0
's in the range 1.9 to 2.4 significant reductions in attack rates to a level where an epidemic may be prevented are only achieved by Germann et al by combining non-pharmaceutical interventions with either targeted antiviral prophylaxis or vaccination, with the exception of child-first vaccination for an R0
of 1.9. Our results suggest that for R0
's up to and including 2.5 epidemics may be prevented by combined non-pharmaceutical interventions alone, provided they are activated immediately and are sustained indefinitely. Given the logistics of vaccination and antiviral drug deployment it is highly likely that non-pharmaceutical interventions may be activated more rapidly and our results suggest a similar ability to prevent epidemic development as that achieved by a combined pharmaceutical/non-pharmaceutical strategy.
The need to react rapidly when activating interventions is also highlighted by Ferguson et al [12
] where antiviral treatment is very sensitive to initial delays of 24 hours, due to the use of an early, peaked infectiousness function. This contrasts with our more abstract flat infectivity profile. Single non-pharmaceutical interventions, such as school closure or home quarantine, are shown to have little impact for R0
in the range 1.7 – 2.0, whilst more significant reductions are suggested in the results that we derive. Similarly, school closure and 50% workplace reduction has less effect (an approximately 4 percentage point reduction in attack rate) in the Ferguson et al model compared to our results, where the suggested reduction in attack rate is of the order of 20 percentage points. While there are clear differences in assumptions between the two models and direct comparison is difficult, key factors may be their requirement to diagnose one case in a school before closure is effected, and their assumption that additional community contact occurs when schools are closed.
The range of modelling estimates for the potential effectiveness of social distancing interventions such as school closure is considerable, and may stem from the range of modelling assumptions about the operation of school closure and associated behavioural changes of individuals [15
]. Observations of actual school closures do not seem to provide conclusive evidence on the effectiveness of school closure. Based on observations made during a teacher's strike in Israel, it was estimated by Heymann et al [22
] that diagnoses of respiratory infections decreased by 42%. In contrast Cowling et al [23
] observed that a school closure episode in Hong Kong in 2008 had little impact on influenza attack rates – although in that case school closure appears to have occurred after the epidemic peak. The largest scale study known to the authors that provides an estimate of the effectiveness of school closure on influenza epidemics is the work of Cauchemez et al [24
]. Based on surveys of seasonal influenza during and between school terms in France, this work estimated that school closure could achieve at most a 17% reduction in attack rates, indicating that school closure may not be as effective as predicted our model.