Bulletin of Mathematical Biology

, Volume 78, Issue 2, pp 293–321 | Cite as

Choice of Antiviral Allocation Scheme for Pandemic Influenza Depends on Strain Transmissibility, Delivery Delay and Stockpile Size

  • Michael Lydeamore
  • Nigel Bean
  • Andrew J. Black
  • Joshua V. RossEmail author
Original Article


Recently, pandemic response has involved the use of antivirals. These antivirals are often allocated to households dynamically throughout the pandemic with the aim being to retard the spread of infection. A drawback of this is that there is a delay until infection is confirmed and antivirals are delivered. Here an alternative allocation scheme is considered, where antivirals are instead preallocated to households at the start of a pandemic, thus reducing this delay. To compare these two schemes, a deterministic approximation to a novel stochastic household model is derived, which allows efficient computation of key quantities such as the expected epidemic final size, expected early growth rate, expected peak size and expected peak time of the epidemic. It is found that the theoretical best choice of allocation scheme depends on strain transmissibility, the delay in delivering antivirals under a dynamic allocation scheme and the stockpile size. A broad summary is that for realistic stockpile sizes, a dynamic allocation scheme is superior with the important exception of the epidemic final size under a severe pandemic scenario. Our results, viewed in conjunction with the practical considerations of implementing a preallocation scheme, support a focus on attempting to reduce the delay in delivering antivirals under a dynamic allocation scheme during a future pandemic.


Antivirals Epidemic Household model Pandemic influenza 



We gratefully acknowledge the support of the ARC (FT130100254 and ACEMS) and NHMRC (PRISM\(^2\)) .


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Copyright information

© Society for Mathematical Biology 2016

Authors and Affiliations

  • Michael Lydeamore
    • 1
    • 3
  • Nigel Bean
    • 1
    • 2
  • Andrew J. Black
    • 1
  • Joshua V. Ross
    • 1
    Email author
  1. 1.School of Mathematical SciencesThe University of AdelaideAdelaideAustralia
  2. 2.ARC Centre of Excellence for Mathematical and Statistical FrontiersParkvilleAustralia
  3. 3.School of Mathematics and StatisticsThe University of MelbourneParkvilleAustralia

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