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. 2007 Aug 16;70(2):382–397. doi: 10.1007/s11538-007-9257-2

A Delay Differential Model for Pandemic Influenza with Antiviral Treatment

Murray E Alexander 1,3, Seyed M Moghadas 1,2,✉, Gergely Röst 4,5, Jianhong Wu 5
PMCID: PMC7088798  PMID: 17701376

Abstract

The use of antiviral drugs has been recognized as the primary public health strategy for mitigating the severity of a new influenza pandemic strain. However, the success of this strategy requires the prompt onset of therapy within 48 hours of the appearance of clinical symptoms. This requirement may be captured by a compartmental model that monitors the density of infected individuals in terms of the time elapsed since the onset of symptoms. We show that such a model can be expressed by a system of delay differential equations with both discrete and distributed delays. The model is analyzed to derive the criterion for disease control based on two critical factors: (i) the profile of treatment rate; and (ii) the level of treatment as a function of time lag in commencing therapy. Numerical results are also obtained to illustrate the feasible region of disease control. Our findings show that due to uncertainty in the attack rate of a pandemic strain, initiating therapy immediately upon diagnosis can significantly increase the likelihood of disease control and substantially reduce the required community-level of treatment. This suggests that reliable diagnostic methods for influenza cases should be rapidly implemented within an antiviral treatment strategy.

Keywords: Influenza pandemic, Antiviral treatment, Delay equations, Epidemic model

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