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Mathematical Medicine and Biology Advance Access originally published online on September 17, 2008
Mathematical Medicine and Biology 2008 25(4):359-372; doi:10.1093/imammb/dqn018
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Evaluating the effectiveness of antiviral treatment in models for influenza pandemic

Antonella Lunelli{dagger} and Andrea Pugliese

Department of Mathematics, University of Trento, via Sommarive 14, 38100 Povo (TN), Italy

{dagger} Email: alunelli{at}science.unitn.it

Received on November 9, 2007. Revised on July 10, 2008. Accepted on July 11, 2008.

We study the effectiveness of antiviral treatment in simple susceptible–exposed–infectious–removed models that are at the base of models used for influenza pandemic. The strategy is assessed in terms of the value of the reproductive ratio R0. We consider a general framework and analyse six different specific cases. The same antiviral strategy is simulated in all models, but they slightly differ in the compartmental structure. These differences correspond to different underlying assumptions concerning the timing of the intervention and the selection of individuals who receive treatment. It is shown that these details can have a strong influence on the predicted effectiveness of the strategy: for instance, with R0 = 1.8 in absence of treatment, different models predict that with treatment R0 can become as low as 0.4 or as high as 1.3; still, in all models 70% of infected individuals are treated and the infectiousness of treated individuals is reduced by 80%. A particular assumption that can be included when modelling influenza is time-varying infectivity. We consider a specific model to verify if the predicted effectiveness of antiviral treatment is influenced by the inclusion of this assumption. We compare the results obtained with constant and variable infectivity, in relation also to the time of intervention. It is likely that existing differences in the predictions of the effect of control measures depend on such modelling details. This finding stresses the need for carefully defining the structure of models in order to obtain results useful for policymakers in pandemic planning.

Keywords: antiviral treatment; influenza pandemic; infectious disease modelling; infection reproductive ratio


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