Elsevier

Mathematical Biosciences

Volume 209, Issue 2, October 2007, Pages 336-360
Mathematical Biosciences

Prophylaxis or treatment? Optimal use of an antiviral stockpile during an influenza pandemic

https://doi.org/10.1016/j.mbs.2007.02.003Get rights and content

Abstract

We introduce a novel mathematical model that effectively incorporates contact tracing in a realistic distribution mechanism for antiviral drugs in an influenza pandemic scenario. A strategy focused on targeted provision of post-exposure prophylaxis, rather than treatment, will provide the greatest chance of minimising the impact of an influenza pandemic. Targeted post-exposure prophylaxis delays the onset of the pandemic and for a wide range of parameter values, a delay of the order of 6–18 months may be achievable. This may provide enough time to develop and distribute a vaccine. In contrast, a treatment based strategy typically does not delay the onset of a pandemic by an appreciable amount and, in general, is not capable of significantly reducing the attack rate from baseline.

Introduction

The threat of a global influenza (H5N1) pandemic in the human population is currently of great concern. The H5N1 avian influenza strain has spread rapidly through the world’s bird population. Both wild and domestic birds have become infected on an unprecedented scale. There is now clear evidence of direct transmission of avian strains to humans [1]. Sustained human to human transmission, sparked by appropriate mutation of the avian influenza virus or a mixing event with a currently circulating human influenza virus, would signal the imminent onset of a new human influenza pandemic. Due to lack of prior exposure, a novel strain of influenza is potentially more dangerous and, simultaneously, more difficult to control than the current circulating influenza strains. An effective vaccine will take some months to develop, manufacture and distribute once a human-to-human strain becomes established in the human population [2], [3]. Accordingly, antiviral drugs, along with various social distancing interventions, constitute a first line of defence in pandemic response plans.

Preparedness planning is of the utmost importance in effectively combating a pandemic, should one arise. WHO has recently revised their WHO global influenza preparedness plan [4] in light of the threat from avian H5N1 (circulating in Asian poultry flocks since 1996) and, to a lesser extent, other avian strains that have recently crossed the species barrier to infect humans, namely H7N3 in Canada, H7N7 in the Netherlands [5] and H9N2 in Hong Kong [6]. Mathematical models are an integral part of the planning process, allowing the consequences of untested (and untestable) strategies to be explored in a systematic and logical way [7], [8]. Mathematical modelling has a long history in communicable disease research [9]. The threat of pandemic influenza provides new challenges, not least of which involves analysis of the optimal use of the world’s limited supply of antiviral drugs.

Some models exploring the effectiveness of antiviral drugs have either focused purely on treatment strategies [10], ignoring the potential impact of prophylaxis, or have not fully taken into account the fact that many courses of the drugs, when provided as prophylaxis, will be apparently ‘wasted’ [11]. That is, they will be provided to contacts of known infectives who would not have become infected. That many courses of antiviral drugs will be used in such a fashion is simply a reflection of the fact that the average number of secondary infections arising from a primary case (the reproduction number) is far lower than the average number of close contacts that the primary case makes over the course of their infectious period. Underestimating this ‘wastage’ will overestimate both the effectiveness of prophylaxis as an intervention and the lifetime of the antiviral stockpile.

The motivation for the model presented is to build just enough structure on top of a standard deterministic Susceptible–Exposed–Infected–Removed (SEIR) model to allow treatment and prophylaxis strategies to be investigated. We do not attempt to model all biological and epidemiological aspects of influenza disease, aiming to keep the model analytically tractable so as to fully understand the outcomes of various intervention strategies.

We discuss the model dynamics and derive threshold distribution conditions to halt the epidemic. To demonstrate the potential of the model structure we use observed data on contact patterns [12] among university students to estimate the number of social contact events that may result in transmission of influenza virus. These are incorporated into the model to predict how many courses of drugs may realistically be distributed for contact based targeted prophylaxis when an infective is identified. The qualitative differences between a treatment strategy and a prophylaxis strategy are explored. We investigate the requirement put on the health system to deliver the proposed interventions and determine the parameters to which the model is most sensitive.

Section snippets

Model structure

The deterministic model presented is based on the SEIR structure, extended in an unconventional but meaningful way to provide for targeted distribution of antiviral drugs. The key idea is to clearly separate two fundamental concepts in a contact tracing strategy:

  • 1.

    Disease status. Is an individual currently S, E, I or R?; and

  • 2.

    Contact status. Is an individual currently (or have they recently been) in sufficient contact with an infectious individual such that they may conceivably contract infection?

Results

For all simulations we only initiate use of antiviral drugs once 10 new cases have been identified on a single day. The rationale is that it takes time both to realise that an epidemic is taking off and to implement intervention plans. We discuss sensitivity to this assumption in Section 3.5.3.

Basic findings

The most important finding from the modelling work presented here is that prophylaxis and treatment strategies lead to markedly different outcomes. While a treatment only strategy may be effective in some circumstances, it is likely that treatment will be largely ineffective (in terms of population level effects) for many pandemic scenarios (Fig. 3 and Section 3.5.2). The results indicate that providing prophylaxis to contacts will, in almost all cases, lead to improved public health outcomes (

Summary

By realistically accounting for drug distribution in targeted post-exposure prophylaxis programs, we have compared treatment and prophylaxis strategies for minimising the impact of an influenza pandemic. From the results, it is clear that a prophylaxis strategy, supplemented with treatment for those who do become infected is the optimal use for an antiviral stockpile in the Australian context. The key conclusion is that, for a range of attack rate scenarios, an efficient contact tracing program

Acknowledgements

We are indebted to James Wood (NCIRS, Sydney) for significant contributions and helpful comments in developing the model structures and on the manuscript. John Mathews (School of Population Health, Melbourne) provided input on plausible parameter choices and, along with Chris McCaw (School of Population Health, Melbourne) and Peter Eckersley (Computer Science, Melbourne), provided valuable feedback on the manuscript. Thank you also to Niels Becker, Katie Glass, Belinda Barnes, Peter Caley and

References (39)

  • W.O. Kermack, A.G. McKendrick, A contribution to the mathematical theory of epidemics, in: Proceedings of the Royal...
  • R. Gani, H. Hughes, D. Fleming, T. Griffin, J. Medlock, S. Leach, Potential impact of antiviral drug use during...
  • N.M. Ferguson et al.

    A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antivirals

    J. Antimicrob. Chemother.

    (2003)
  • W.J. Edmunds et al.

    Who mixes with whom? A method to determine the contact patterns of adults that may lead to the spread of airborne infections

    Proc.: Biol. Sci.

    (1997)
  • W. Al-Nakib et al.

    Prevention and treatment of experimental influenza a virus infection in volunteers with a new antiviral ICI 130

    J. Antimicrob. Chemother.

    (1986)
  • F.G. Hayden et al.

    Local and systemic cytokine responses during experimental human influenza a virus infection. Relation to symptom formation and host defense

    J. Clin. Invest.

    (1998)
  • I.M. Longini et al.

    Containing pandemic influenza with antiviral agents

    Am. J. Epidemiol.

    (2004)
  • C.B. Hall et al.

    Children with influenza a infection: treatment with rimantadine

    Pediatrics

    (1987)
  • W.J. Edmunds et al.

    Mixing patterns and the spread of close-contact infectious diseases

    Emerg. Themes Epidemiol.

    (2006)
  • Cited by (0)

    View full text